The weed killer they had been using for more than 40 years had caused them to become cancer.

英訳に間違いが有れば正してください。

彼らが40年以上にわたって使用してきた除草剤が、彼らに癌を発生させた。
The weed killer they had been using for more than 40 years had caused them to become cancer.

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答え becomeをgetにする

The weed killer they had been using for more than 40 years had caused them to get cancer.

become+病気で病気になるという表現はない。

get cancer
癌になる