I once had the latter happen but because I had three items. One item was my shoulder bag with my computer and a small overnight kit. The other two boxes had glassware that combined were similar to a medium sized roll aboard. So nothing outrageous. I tied string around each box so to make them easy to carry. The GA was having no thing to do with it. So I took my computer and overnight kit out, gave them my now empty shoulder bag, and walked on to the plane. A few minutes later the GA came on board and gave me shoulder bag back.