The first number, such as the “5” in 5W-30, indicates how the oil flows in cold temperatures (the “W” stands for winter). A lower number means thinner oil, which circulates faster during cold starts, making 5W-30 better for cold climates compared to 10W-30
The second number, like the “30” in both 5W-30 and 10W-30, represents the oil’s viscosity at high temperatures (tested at 212 F). At this temperature, thicker oil like 30-weight oil clings to and protects engine parts better when the engine is hot and operating under stress.
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Get a compression gauge and end the guesswork. It will not tell you where the compression leak is, but just that it exists. The smoke could also be bad valve guides letting oil into the combustion chamber or worn piston rings, etc.
Checking your head gasket is an easy thing. If it's bad you can usually see a gap and/or discoloration where the "blown" area is.
I strictly follow Briggs' recommendations for the 130200 series (your engine) in terms of torque settings and the tightening sequence for reinstalling the cylinder head.
If you want a link to the Briggs L-head manual, let me know.