Briggs and Stratton recommend and sell under their own brand a synthetic 5w30 oil for their mowers. They say that multigrade dino oil will show some consumption versis a 30w dino.
I have one of those Honda 5.5 hp OHC engines on my mower, purchased in 2000. After the 5 hour break-in with 30w furnished with the mower, it has seen only Mobil 1; 5w30 until last year, and last year I had a quart of 0w30 M1 and decided to use it, just to see if it would lead to increased consumption, since in the previous years I had not had to add a drop of oil. I put it in in March of 2005, and, 64.7 hours of use later, I changed it in March of this year.(I have an hour meter on this mower). The dip stick showed less than 1/16th inch of consumption; probably most of this was used up in checking the oil and wiping off the dip stick. All I had in stock this year was M1 5w30, so I used that.
Remember one thing about these small air=cooled engines: Most,if not all, of them use an oil slinger on the crankshaft to spread the oil around for lubrication. If you are using 30w or 15w40, the oil is much harder to sling than a 0w-or a 5w30. It burns more gas, and puts out less power because of the power absorbed by the thick oil. Just my theory.