How many watts will a home current 15 amp circuit support? Is a 20 amp circuit simply pro rata greater

1800 watts of load that runs less than 3 hours, 1440 watts for a load that runs 3 hours or more.

A 20 amp is 2400 watts and 1920 watts respectively.

Any load that runs 3 hours or more rates the wire and breaker at 125% of the load.