I wouldn't place any worries on the height - but I do have a short boy who is not grade skipped in middle school and part of the reason we've never pushed for a grade skip is related to believing that for our ds, the social issue would be a concern - which honestly is something that is going to vary a lot depending on the individual child, and I'm not sure I would have been able to forward-predict the imp act it would have made on my kids, hence you basically just need to do what feels right to you for your family and child if you're making that decision when your child is still in early elementary.
Rather than grade skip we've sought differentiation and subject acceleration for ds, as well as putting him into an academically challenging school where the full class is working a grade level ahead - there can be other ways of dealing with the need for academic challenge - and granted, we haven't always been terribly successful at it! But fwiw, in the classes our ds has been in where he's subject-accelerated but they aren't necessarily "gifted" classes, he's still been bored, and I'm not sure that a full-grade skip would have completely met his need for intellectual challenge.
The social issues that I've seen in middle school which I think would have been tough on ds had he been younger than his peers resolve around the kids who are becoming aware of their sexuality, starting to think about dating, growing independence from their parents etc. I didn't see it way back when, but I know today that my ds is on the lower-developing end of the curve re interest in those things, and I've also seen that being gifted sets him apart in school in some ways (and he still appears very much gifted when he's in among older kids). Fitting in is very important to him right now (as it is with many kids who are middle school age)... so for him, being with same-age peers has helped out. *BUT* I don't know that I could have known that looking forward when he was only 5.
I have a good friend who did grade-skip her dd (dd is MG) - and her dd has done really really well academically - but now that she's in middle school, her *parents* are having a lot of issues with her classmates being interested in boys, dating, independence from parents etc - all things that I remember us discussing might happen way back when.... and she honestly says now she wished she had thought it through instead of being so focused on the academics.
Last thought re height - if you made the decision based on height alone, how would you feel about your ds knowing you didn't place him ahead due to his height? If you have some reservations about that, I'd take height out of the equation and just focus on the other reasons for/against a grade skip.
Best wishes,
polarbear
ps - fwiw, two of my three kids are very short. It has bothered both of them at times - but if they are really short, they are really short no matter whether or not you're switching them around 1-2 grade levels ahead or behind where they should be placed according to age. I'm also really short, and I wouldn't want someone making a decision about school based on my height.