Most Briggs engines in that size range don't even have an oil pump. They have a "splasher paddle wheel" thingmajig instead. In any case, there is no line that goes from an oil pump to the carburetor. What you're looking at is almost certainly a breather hose that vents the discharge from the PCV valve, not to the carburetor, but to the intake.
The most likely problem is that you have overfilled the crankcase with oil. The PCV (positive crankcase ventilation) valve is designed to release pressure and oil vapor from the crankcase; the hose feeds the discharge to the intake and the oil vapor is then sucked in and burned along with the gasoline. On Briggs motors that size, the PCV valve is generally mounted in the front of the engine block, not all that high above the oil reservoir. It may appear to be an oil outlet of some sort, but it isn't. If you overfill the crankcase with oil, the liquid oil can reach the PCV valve -- which it should NEVER do -- and you will have problems very much like you describe.
I've had a number of customers with similar problems that cropped up right after they changed the oil in their own engines. Instead of using the dipstick to gauge the amount of oil in the crankcase, they went by the book and dumped the specified quantity of oil into the engine. Unless you literally turn the mower on its side, you cannot drain all the oil out of one of these Briggs engines. The oil remaining gets added to the specified amount of oil you dumped in..... and you've got too much oil in the crankcase.