I think it's because there are less people with "extreme" heights, as in very small or very tall. Fat people are much more numerous so they have more voice to "protect" themselves.
Also it's more fat women who have issues with the image, and we all know it's a more of a risk to make fun of women for any reason, and especially their looks. Plus height is part of the social construct of what makes a a man "a man", so it really doesn't affect women that much.
Add to the fact that weight issues are also health issues, and now it's not "fat" or "skinny" but "obese" and "anorexic" and all of sudden you find yourself making fun of someone's illness, which obviously is a no-no. (Notice this also concerns more women than men). Health issues concerning height are less talked about, even though they exist.
If we want to get a little technical back in the day short people being mocked can be traced all the way back, in Europe, to Northern Europeans, which has been more developped for centuries now, making fun/discriminating Southern Europeans, who happen to also be shorter in general. That mentality must've travelled to the US. In Central Africa the short people are pygmees, who are discriminated against/mocked because they are a minority, who happen to be shorter than the rest of the population.
All in all I think these elements somewhat explain why it's it's socially more "acceptable" to make fun based on height.
