First off, I think you got the actors the wrong way round.
I ended up getting fat again.
That's because you eat nothing but sweets.
Can you remove からだ? Grammatically you can, but it wouldn't sound natural in the same way that this English exchange would sound slightly awkward:
A) I ended up getting fat again.
B) You eat nothing but sweets.
B's reply doesn't feel like part of the conversation does it? It just sounds like a random statement of fact.
Edit: I've just realised your problem. You thought からだ was 体 meaning body. But it isn't. It is から meaning 'because' plus the copula だ.