The centrifugal weight gov is in the crankcase. It is driven by a cam gear. On Many Vertical shaft engines it doubles as the oil slinger for engine lubrication. On horizontal engines it is simply a gov. It has absolutely no similarity to the air vane gov except for the control spring which indeed can be tweaked to alter maximum speed by bending the mounting tab on many engines. On others bending a tab is not possible but other forms of adjusting are incorporated.

Air vane governors are the cheapest and simplest and also the least responsive/accurate. Any of them you need to make sure they are working right before tweaking on the control spring. Sticky linkage on all, clogged cooling fins on air vane types, Static setting and internal parts on mechanical/flyweight/centrifugal weight types.

All but a couple of low end Briggs no longer use air vane types. There is a third type used on gen-sets where even more accurate engine speeds are desired. These are electic servo governors. This style uses what in effect are computers that process info and tells the servo where to set the carb throttle. These are found, amoung others, on Honda's Invertor style gen-sets.

Your Honda GCV-160 can have virtualy any of the problems as Imention before. However, based on experience the problem is likely an assembly caused situation. The link between the gov arm and carb only works with one orientation, flip the link and it binds. Installing the jig saw puzzle of insulator block, gaskets and heat shield behind the carb can cause an air leak which causes a lean run and possible over revving. The carb bowl drain tube can interfer with the gov spring if not assembled right. If the gov arm was loosened or removed from the output shaft it needs to have the static setting re-done. These are all incorrect assembly caused problems that I often see from well meaning DIY'ers.