[AT] Briggs stumbles when load increases

[Len Rugen]

I have a 8 HP I/C Briggs that is about 15 years old but has been well cared for.  It starts on the first pull and doesn't use any oil.  Its problem is that when a load hits it, it "stumbles" and nearly dies, then runs rough for awhile.  If the load stays constant, it will handle it, but if it varies, it runs bad.  It has a float carb, and will leak when not running unless I turn off the fuel, so I know it needs at least a float valve.  

What else could it be?