Your resume is yours. While you need for it to be an honest description of work history and skills and qualifications, it is still YOUR sales pitch.
A useful analogy is when your spouse/partner asks you about your day. If you start with your morning coffee and end with putting on your coat at the end of the day, well, that’s probably more than they really care to know. They want highlights, and if we’re all being honest both they and you want the highlights that cast you in a positive light (they chose you, remember). By the same token, if you leave out that you had a lunch date with an ex, they might not take it well if they later discovered that omission.
So, put the stuff on there that matters and that sells you. A three week stint is a waste of everybody’s time and effort, including mine when I’m trying to decide who to call for an interview.