Translation:I am not used to the weather here.
This seems to accept both "I am not used to the weather here" and "I can't get used to the weather here".
Would there also be ways to distinguish between those two sentences in Chinese?
Flexible translation of “can” again… To emphasize the personal inability rather than the state, we can replace “不” with “无法 / 没办法 / 不能”. “不可以” is not so good because it sounds more like “not permissible to” for this sentence. Similarly, “不能” is passably okay.