It can impact the memory of runtime-oriented languages, especially if they keep the text around (e.g. for reflection or whatever) but that's about it.
Writing and then maintaining comments is an expense. Your compiler doesn’t check your comments so there is no way to determine that comments are correct. You are, on the other hand, guaranteed that the computer is doing exactly what your code is telling it to.
Unless your team has the discipline to maintain them, don't litter the code with comments. Put it in the commit message. Obsolete and incorrect comments are just confusing.
What I sometimes do is write comments before I implement something. This provides a clear idea of what I need to do and where. Then when it's done I cut it into commit message or note