Airlines limit a carry-on bag to a maximum number of linear inches that will fit in most airplanes' overhead compartments. The linear inches are calculated by adding the length, width and height of the bag in inches. Baggage allowed as a carry on can be up to 55 linear inches.
Airlines ask that heavier items be placed underneath the seat in front of you rather than in the overhead compartment. Many airlines do not limit the weight of a carry on, but Delta, for example, limits the weight to 11 lbs..
If your carry on is too large to fit in the overhead compartment, the airline may take the item away from you and return it upon arriving at the destination. Additional charges may be added for this baggage and the inconvenience of it not fitting in the compartment.