あまり and 過ぎる both indicate an excess of something, so saying あまり食べ過ぎる seems redundant and the equivalent of "eat too too much." However, a sentence like this occurs quite often. Is there actually any difference in meaning compared to simply saying 食べ過ぎる or あまり食べる?
By using similar words twice, it says the excess is even more excessive. For example,
If you just eat a little too much, that's OK, but if you eat really too much, you'll get a stomachache.