The new enforcement policy began last Saturday, the Chicago Tribune reported.
The airline allows passengers to board with one carry-on and one "personal item" like a backpack, laptop bag or shoulder bag. Carry-on bags can be no larger than 14-by-22 inches and personal items no more than 10-by-17 inches, with 9 inches the maximum depth for both.
The airline charges most passengers $25 for each checked bag, but Rahsaan Johnson, a spokesman, said United is not trying to squeeze them for revenue.
"This change is to address the frequent complaints that we get from customers who tell us they are playing by the rules but we are not able to accommodate their bags because other customers are not -- and that we should be enforcing them," Johnson said.