Quick googling result: http://frac.org/initiatives/hunger-and-obesity/are-low-incom...
e.g. just this week http://www.bbc.co.uk/news/uk-politics-21158087
There is no need for speculation, since we already know the answer: fast-food is both affordable and calorie-dense, which is why lower-income people consume it and become overweight.
Ever noticed how many fast-food restaurants there are in lower-income neighborhoods?
Fast-food is not affordable in the UK. It's substantially more costly than preparing your own food. There is no way that we could afford to eat fast-food more than a couple of nights per week; then we'd have to cut the quality of food on other nights considerably.
McDonalds for one adult costs about what we spend on a meal for 4 cooked at home (not including energy costs).
That said friends we have friends on benefits who eat fast food regularly. How they afford it I don't know. They have the heating on all day (with windows open, in winter) and things too, it's all a mystery to me.
Height is doubtless correlated with athleticism, but it's fairly weakly correlated. Except in basketball, when you see a group of athletes, you'll tend to see a range of heights. A little taller than average? Sure. But not immensely so.
And then, athleticism is doubtless correlated with admission to elite universities, but, again, only weakly so. The top tier and second tier universities like to see some extracurricular activities on your record, but "being good at cross country running" is far from a sure-fire way to get into Harvard. The REALLY good athletes don't go to top-tier academic universities, and don't get corporate jobs -- they're on the pro athlete track.
You might get into Harvard due to being a good football player but not good enough to go pro, even if you were not otherwise academically capable of going to Harvard. But, first, you're now talking about a small percentage of Harvard students. Second, I'd like to see some data before I'd concede that IF you're clearly not elite-university quality academically, BUT you get in on your athletic merits, AND you go into a corporate track job, THEN you end up with an elite career path.
So, long story short: Is there probably some advantage to height through the path you suggest? Yes, probably some measurable advantage. Is it enough to explain the pretty substantial advantage that tall men enjoy according to the literature? I can't see how. It's passing through too many weak correlations.