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She's on a diet because she doesn't want to gain weight.
Literal
She [topic-は] body-weight [subject-が] increase [if-no-good-といけない][because-から] diet [object-を] is-doing.
~といけない ('if X, that's no good / mustn't X / it would be bad if X') is the conditional ~と + the negative-evaluative いけない. Literally 'if X happens, it's no good,' it expresses a worry or aversion — close to 'don't want X to happen.' Here 体重が増えるといけない ('it'd be bad if she gained weight') gives the motivation. ダイエット is a katakana loanword whose Japanese meaning is more specifically 'weight-loss diet / weight-loss regime' (not the broader English 'diet' meaning eating habits).