You asked
Does sensor size affect background blur?
Yes, it does. At the same framing and the same f-number, a bigger sensor gives you more background blur. An f/1.8 lens on APS-C gives about the depth of field of f/2.8 on full frame, so full frame has the edge for shallow focus.
That gap is smaller than people expect, though. A fast APS-C lens closes most of it for far less money, and the things you control matter just as much: a longer focal length, getting closer to your subject, and putting more distance between them and the background. Moving your subject away from a wall often does more than a faster lens.
For the full picture, see sensor sizes and portraits.
Written by Claude from this site's pages.