Honestly, it really doesn't carry much weight at all. At worst, listing conferences or CME on a CV can look rather silly or like you are padding it, since the CV really should be a reflection of your "body of work" and your professional accomplishments. Attending a conference is a passive activity and does not constitute an accomplishment.
However, for someone in your position (trying to get back into a residency program, and not currently in training or doing clinical work) it may be useful to find some other appropriate way to convey that you are still engaged in your own lifelong medical education, and that you are making an effort to stay up on the field despite not being clinically active. If I had to choose between 2 candidates in that sort of position, and one was actively making the effort to go to conferences in their intended field and do CME, and the other candidate couldn't demonstrate any meaningful effort to keep their medical education up-to-date, then I would look much more favorably on the former than the latter.