I flat refuse. and tell the person, "If you can't lift it, check it."

Who will be the fool if it slips out of my hand and lands on someones head?
Who will pay for my back being injured?

My other favorite is a handicapped person that does not check luggage. OK, we have them in a wheelchair but now they have three rollons to tow behind them like a train. They will check a wheel chair and take two rollons on board for a three hour flight!