B&S 3.5 starts running lean at 1/4 tank

I've got an older B&S 3.5 on a lawn mower which seems to run lean as I get to about 1/4 tank. It's the common base engine with the carb attached to tank. It starts to idle down as it gets around 1/4 tank; bogs much more readily if I hit some thicker grass. I fill it up and it runs fine.

Any thoughts on an easy/cheap fix? Otherwise I can deal with it, but invariably I'm almost done when this happens, and I have to fill the tank up when I'd otherwise be able to finish the job without stopping.