I'm a native British English speaker and "She hates to work at weekends" sounds fine to me, as do "She hates working at the weekend", "She hates working weekends" and various other permutations. "on weekends" and "on the weekend" are not natural to me. I can't really advise on US usage, but looking at Google news hits it seems there's a definite bias towards "at" in UK publications and "on" in US publications.
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