git diff HEAD 'HEAD@{3 weeks ago}' -- some/file/path/file.ext
This is not, strictly speaking, the revision made three weeks ago. Instead, it’s the position HEAD was at three weeks prior to the present. But it’s probably close enough for your purposes – it will be very accurate if the current branch’s HEAD moved forward steadily, as most tend to do. You can improve the accuracy by using a branch name instead of HEAD.
Instead of an offset-from-the-present, you can also use a date/time, like HEAD@{1979-02-26 18:30:00}. See git help rev-parse.