I already had TableLayout="Fixed" in my MasterTableView, but all columns had specific widths defined, thus the grid was always a constant size. So I put specific widths only on the columns I do NOT want to resize and left the columns I do want to resize with no width attribute. Doing this alone did not quite work without the Resizable="false" setting on the columns I do NOT want to resize.
Thank you both. My RadGrid is now behaving as I want.