Birth Order and Height

The association between height and birth order: evidence from 652 518 Swedish men

"birth orders 2, 3 and 4 were associated with 0.4, 0.7 and 0.8 cm shorter height than birth order 1, respectively{Being the first or only child is important for greater height}. The associations were similar in large and small and high-SEP[socioeconomic position] and low-SEP families, but were attenuated[diminished] in recent cohorts[groups]. Birth characteristics did not explain these associations. "

There is one study mentioned that shows the reverse trend where children born after other kids are taller.

I'm not sure exactly what conclusion you can draw but it shows the importance of the maternal conditions on the health of the child.