ok. depending on the type of carb there are several easy fixes.
If the carb has a bowl under it chances are your float is stuck.Or it could be that your Valve Float Needle has a bad seal. These are cheap to fix.
Go to your local lawn mower supply with both the float and needle. You might want to have the model number of the engine hand just in case.
They should be able to hook you up with OEM replacements for less than $20
If it's a tank type carb you might be better off replacing the whole carb. 90% of Briggs tank type carbs are plastic and will run you less than $40
I hope this answer helps...Good Luck