Ok, here's your engine (an opposed twin):
https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/briggs-stratton/briggs-stratton-engine/400000-699999-series/402700-to-402799/402707-1212-01/air-cleaner-group-fuel-hoses How long have you owned this machine?
If it's "new" to you, it's very possible someone's been in the carb and dinked with it.
Could have left a gasket out, a worn gasket, "opened up" a jet, etc.
If need be, print the carb parts diagram out and remove your carb. Start comparing your assembly
to the diagram and any abnormalities..
You could have a leaky carb needle / seat as well.
Do you have a fuel pump? If so, check for any leakage from the pulse hose into the crankcase.
You may also want to just un-bolt the carb from the manifold, line hooked up and fuel turned on.
Then monitor for any leakage.