The Main Jet in the carb is clogged.
Give engine MODEL & TYPE numbers and one can probably give better instructions on how to clean it.

Thank you kindly, Bill. The engine is an Intek Pro 6.5hp OHV, Model No. 122672, Type No. 0128E1.

You lucky dog! You have one of the easy ones!!

The brass nut holding the carburetor bowl on IS the Main Jet.
Clamp off the fuel line or drain the tank.
Remove Nut.
It'll have one or more TINY little hole(s) in it.
Use a fine wire (like a wire tie from a loaf of bread) and clean out the hole(s).
Sometimes a clogged hole looks like a black "spot" and not a hole.

Thanks again, Bill. You're right - the access could be a lot worse. The bad news is that, on the BG, the deck extends out in front of the engine, so there's not much space between the bottom of the carb bowl and the deck. It will have to wait for now - I have some hernia surgery coming up. But once I get that little condition fixed, maybe I can drop the deck to its lowest setting and get the nut out.