I have a Briggs 9hp. Wanna say its a late 90's or early 00's. I let motor sit all summer and got rust in gas tank. I replaced gas tank, fuel lines, filter and oil. I also removed carb bowl and sprayed SEAFOAM around float tube and in carb. My motor runs great while sitting level. But once I lower prop in water or air it runs for about 20 seconds and shuts off. Then I get it back to level and it starts on first pull. I read it could be oil levels to low, but I tried that with no luck. I even took carb bowl off and tilted motor back and gas continued to flow from carb. Motor runs perfect when level it shuts off when prop in lowered. I can even run in water at full throttle but I have to keep prop almost out of water. Any help. I removed the mercury tilt switch a while back..... Don't think that would matter....

Update.... So I took the carb out and found a small bit of junk inside. I cleaned it out and put back together. Runs a little bit longer with prop lowered but still shuts off after a little while.

Even though you cleaned the carb, it still sounds like a carb issue

DIP time for the carb and rebuild kit and start using chevron 93 from now on...

possible worn out carb / engine - he did say 90's early 00's

Carbs don't wear out but they do plug up... Buy a gallon of DIP and
take it apart and soak it in the DIP - it eats out the crud - and plastic
and rubber so you have to take it apart and DIP all the metal parts
and jets...

Take a can of spray carb cleaner and blow thru all the lil passageways
and venuri openings before and after DIPing...

Your idle passages are different from the hi speed ones on most carbs...
Sounds like it is starving for fuel on the hi speed side and or the float
is not fully opening up... Also check and buy a rebuild kit for the fuel
pump as most just have a rubber diaphram and check valve and work off
the motion and wind off of the piston going back and forth...

I had a 1970s GDLT and the pump and carb kits were easy to find at
an air cooled motor / lawn mower shop - just take down all the motor
numbers and take the odd parts and carb with you to match everything up....

Also if it has points and condenser upgrade it to a stator - they run way
more reliably afterward.... The air cooled guys can help you with that too...