Is it possible to grow taller by gaining more body fat?

Some people have asserted that fat people tend to be taller.  They have speculated that it may be due to an abundance of nutrients or that adipose tissue acts on the human body in such a way as to result in a taller individual.  Body fat can reduce insulin sensitivity and this may lead to an increase in height(likely through an IRS-1 related mechanism which controls chondrocyte differentiation).  Leptin which is produced by body fat has anabolic effects as well.

In humans, adipose tissue is located beneath the skin, around internal organs, in bone marrow(you can reduce these levels by supplements like Vitamin D), and in breast tissue.  Skin is located at both the top of the head and the bottom of the feet.  An increase in body fat in the head would result in an increase in body height(but we all know how body fat likes to be stored closer to the center of the body rather than in the extremities).  An increase in body fat in the skin in the feet would also result in an increase in height but it would likely be compressed as a result of your bodyweight pushing down.  It would, however, result in an increase of your laying down height(your height measurement taken from heel to top of your head when you are laying down eliminating compression forces).

Adipose tissue is also located in bone marrow.  How much is based on chemical and mechanical stimulatory factors.  Adiposal stem cells do have the potential to differentiate into height increasing cells.  

Fat mass is negatively associated with cortical bone size in young healthy male siblings. 

"Total and regional fat mass were found to be inversely associated with areal bone mass and bone size, independent from lean mass (radius periosteal circumference beta: -0.29 +/- 0.04). Lean mass was positively associated with bone size but inversely with cortical density at both tibia and radius. The negative association between total fat mass and bone size was independent from sex steroid concentrations. Leptin but not adiponectin was inversely associated with bone size[this goes against our previous results which show Leptin can have height increasing effect, adiponectin is a chemical that "burns" fat], but this was no longer significant after adjustment for body fat[so given the same body fat levels, the person with higher leptin will be shorter].
Increased fat mass is associated with smaller bone size, challenging the view of a high bone mass index as a protective factor for osteoporosis, whereas lean mass was a consistent positive determinant of bone size."

But this conclusion that fat mass is negatively associated with bone size is not made in this study...(and of course other studies show that leptin has positive benefits on bone size).  There are studies that show that Leptin can reverse the inhibitory effect of diet on growth.  What's interesting though is that fat mass has an effect on bone independent of hormones such as leptin.

How does body fat influence bone mass in childhood? A Mendelian randomization approach. 

"Fat mass may be a causal determinant of bone mass, but the evidence is conflicting, possibly reflecting the influence of confounding factors. The recent identification of common genetic variants related to obesity in children provides an opportunity to implement a Mendelian randomization study of obesity and bone outcomes, which is less subject to confounding and several biases than conventional approaches. Genotyping was retrieved for variants of two loci reliably associated with adiposity (the fat mass and obesity-related gene FTO and that upstream of the MC4R locus) within 7470 children from the Avon Longitudinal Study of Parents and Children (ALSPAC) who had undergone total body DXA scans at a mean of 9.9 yr. Relationships between both fat mass/genotypes and bone measures were assessed in efforts to determine evidence of causality between adiposity and bone mass. In conventional tests of association, both with and without height adjustment, total fat mass was strongly related to total body, spinal, and upper and lower limb BMC (ratio of geometric means [RGM]: 1.118 [95% CI: 1.112, 1.123], 1.110 [95% CI: 1.102, 1.119], 1.101 [95% CI: 1.093, 1.108], 1.146 [95% CI: 1.143, 1.155]; p < 10(-10) [adjusted for sex, height, and sitting height]). Equivalent or larger effects were obtained from instrumental variable (IV) regression including the same covariates (1.139 [95% CI: 1.064, 1.220], 1.090 [95% CI: 1.010, 1.177], 1.142 [95% CI: 1.049, 1.243], 1.176 [95% CI: 1.099, 1.257]; p = 0.0002, 0.03, 0.002, and 2.3(-6) respectively). Similar results were obtained after adjusting for puberty, when truncal fat mass was used in place of total fat, and when bone area was used instead of bone mass. In analyses where total body BMC adjusted for bone area (BA) was the outcome (reflecting volumetric BMD), linear regression with fat mass showed evidence for association (1.004 [95% CI: 1.002, 1.007]). IV regression also showed a positive effect (1.031 [95% CI: 1.000, 1.062]). When MC4R and FTO markers were used as instruments for fat mass, similar associations with BMC were seen to those with fat mass as measured by DXA. This suggests that fat mass is on the causal pathway for bone mass in children. In addition, both directly assessed and IV-assessed relationships between fat mass and volumetric density showed evidence for positive effects, supporting a hypothesis that fat effects on bone mass are not entirely accounted for by association with overall bone size." 

In the study they mention that neither genotype was shown to affect height.  Fat mass seems to have the greatest impact on periosteal growth(which could make you taller at the top of your head and soles of your feet).

So it seems as though adipose tissue cannot increase height except in a very minor fashion at the extremities of the body(both by increased periosteal deposition and by possible fat storage there).  Any adipose tissue effect is likely related to hormonal factors such as leptin.


Update on statural growth and pubertal development in obese children

"During pre-pubertal years, obese patients present higher growth velocity and that this pre-pubertal advantage tends to gradually decrease during puberty, leading to similar final heights between obese and non-obese children. Excess body weight might also influence pubertal onset, leading to earlier timing of puberty in girls."

"during pre-pubertal years, obese children present higher growth velocity and accelerated bone age compared to lean subjects. However, this pre-pubertal advantage in growth tends to gradually decrease during puberty, when obese children often show a reduced growth spurt compared to lean subjects. This latter effect, together with early pubertal maturation in obese children, determines similar final heights between obese and non-obese children."

"an increase in BMI of 1 unit led to an increase in height of 0.23 cm in boys and 0.29 cm in girls between ages 2 and 8 years. In addition, an increase in BMI of 1 unit reduced pubertal height gain of 0.88 cm in boys and 0.51 cm in girls, resulting in no beneficial effect on final height."

"Obese youth show a reduction in GH half-life, frequency of secretory bursts and daily production rate of GH.12 In particular, daily GH secretion and production rate have been calculated to fall by 6% for each unit increase in BMI, and 50% for an increase from 21 to 28 kg/m2. GH secretion is also impaired in response to all traditional stimuli acting at the hypothalamus. However, although GH secretion is blunted in obese children, their GH responsiveness appears to be increased compared to normal weight youth. At the peripheral level, increased GH binding protein (GHBP) values, corresponding to the extracellular domain of GH receptor, have been described in obesity"

Body fat in children does not adversely influence bone development: a 7-year longitudinal study (EarlyBird 18).

"A cohort of 307 children was measured biannually from 9-16 years for height and weight, and every 12 months for percent BF, bone area (BA), bone mineral content and areal bone mineral density (aBMD) by dual-energy X-ray absorptiometry. Pubertal tempo was determined quantitatively by age at peak height velocity.
Percent BF increased and then fell in the boys, but increased throughout in the girls. aBMD and BA increased in both genders. Greater BF was associated with higher aBMD and BA in girls, but only BA in boys. The extra aBMD associated with increased BF was greater in older girls. The rise in aBMD and BA was associated with earlier puberty in both genders. The impact of BF on aBMD was greater in later puberty in girls (0.0025 g cm-2 per 10% BF at 10 years versus 0.016 g cm-2 per 10% BF at 14 years).
Greater BF is associated with larger bones, but also denser bones in girls. The effects of fat and puberty are complex and gender specific, but BF of contemporary UK children does not appear to be deleterious to bone quality."

"On one hand, the extra mechanical load [of fat] leads to periosteal expansion and greater bone mass, while on the other the inflammation associated with obesity can lead to bone demineralization "<-both inflammation and periosteal expansion can affect height growth.

" In boys, the fall in BF noted [at age 15/16] occurred later in those whose growth spurt arrived later"

"the peak BF achieved was substantially greater among those whose APHV[Age where peak height velocity was achieved] was later"