After 15 years, that engine needs a full service. Things like:
1.Remove top engine/flywheel shroud/cover and clean the cylinder block cooling fins of grass, oil, dirt and bugs. Make sure the bottom of the cylinder/s is clean and free for air movement.
2.Dump fuel tank and clean out with pure ammonia. Shake it around real good. Dump that out and refill with ammonia. If it needs it let it soak.
3.Install new fuel lines and filter
4.Valve clearance adjustment
5.Run fuel stabilizer year round
Was this a new OEM Briggs carb or a Chinese carb? Definitely sounds like a carb issue.
slomo