Look taller with better posture

Angular and linear spinal parameters associated with relaxed and erect postures in healthy subjects

"Thirty young women and men were measured twice over a 1 week interval for recording the cervical, thoracic, and lumbar curves values using an ultrasound-based system. Thereafter, additional 28 men and women extracted from the same reference group were assigned for a single measurement session, in which the same angular values were obtained in relaxed and fully erect standing postures, as well as stature using stadiometer. Excellent, good, and poor reproducibility indices, standard error of measurement (SEM), and smallest real difference (SRD), were noted for the thoracic (interclass correlation coefficient, ICC(3,3) = 0.95, SEM = 1.2°, SRD = 3.3°), lumbar (ICC(3,3) = 0.85, SEM = 2.6°, SRD = 7.2°), and cervical (ICC(3,3) = 0.68, SEM = 3.8°, SRD = 10.5°) curves, respectively. Erecting from relaxed posture was associated with a significant (>SRD) thoracic angle difference of 7.2° in men and 4.8° in women which was expressed in a height increase of 1.3 cm[about half an inch] in men and 0.8 cm in women. These changes were significantly larger in men in whom the angular and height differences were also significantly correlated (r = 0.7)"

So a pretty significant increase in height just from better posture.

Prolonged and repeated upright posture promotes bone formation in rat lumbar vertebrae.

"Both forelimbs of rats were amputated and these rats were kept in the custom-made cages to keep prolonged and repeated upright posture. Changes of bone were observed in the lumbar vertebrae at three different time points after the surgery. To investigate the effect of prolonged and repeated upright posture on bone formation of rat lumbar vertebrae.
Previous studies show long-term and repeated load-induced bone formation, but there are no clear evidences to indicate whether or not long-term and repeated assumption of the upright posture could result in bone formation at rat lumbar vertebrae.
The forelimbs of 30 rats were amputated when they were 1 month old. These rats were kept in the custom-made cages and were forced to stand upright on their hindlimbs and tails to obtain water and food. Normal rats of the same ages kept in regular cages were used as control. The rats were sacrificed at 5, 7, and 9 months after the surgery and lumbar vertebrae samples were harvested for micro-computed tomographic (CT), histological, and immunohistochemical studies. Total RNA isolated from these samples were used for real-time polymerase chain reaction of type I collagen (Col1α2), type X collagen (Col10α1), transforming growth factor-β1 (TGF-β1) and its related nuclear transcript factor runt-related transcription factor 2 (Runx2), as well as the biomarker of angiogenesis and vascular invasion, which is also a prerequisite for endochondral bone formation: vascular endothelial growth factor (VEGF).
Micro-CT and histological studies showed increased trabecular bone density and increased osteoblast quantities of lumbar vertebrae after surgery. Immunostaining revealed increased protein expression of type I collagen, type X collagen, TGF-β, and VEGF. Real-time polymerase chain reaction showed upregulated expression of Col1α2, Col10α1, VEGF, TGF-β1, and Runx2 mRNA.
Upright posture induces bone acquisition in the rats' lumbar spine, primarily through the mode of the endochondral ossification, which is associated with increased loading, activated VEGF, and TGF-β1 signaling."

Endochondral ossification is how height increases as well.  Unfortunately I could not obtain the full study which would be important for clarity here.