Fundamentally power comes from how much air/fuel mixture you can shove through the engine
from inlet to exhaust
. Let's leave aside nitrous oxide and such for the time being.
Imagine the inlet to the exhaust
as one pipe. The way to get more air though is to turn the engine
faster (higher RPM) or compress the air on the front side (turbo or supercharging). You still have to get it out the back side.
A normally aspirated (non turbo) engine relies on ambient pressure to "push" the air through the inlet into the combustion chamber. As the piston goes down the cylinder the pressure drops and ambient pressure outside pushes air through the carb.
As it goes through the throat of the carb (venturi effect) a low pressure allows ambient pressure to push fuel
from the carb bowl into the air. The size of the throat and the size of the fuel
nozzle ensures the proper mix.
By putting a bigger carb on the engine you open up the inlet but have done nothing to improve the passage
by any valves, the head
through the combustion chamber and out the exhaust.
There may be a slight improvement due to a freer breathing (bigger) inlet but you could acheive those gains with a low resistance air filter.
There is a risk with switching to a bigger carb of changing the mixture as the carb depends on the pressure drop through the throat to draw in the fuel.
At a minimum you would have to increase the exhaust capacity to want to see any improvement.
All of this is caveated by the total design of your engine. There could be gains but nothing you would write home about. The 6 hp carb could also be an alternate but you'd need to see the parts
book to believe that one.
If I was stuck in Vanuatu
and the only carb available was one for a 6hp. I'd go for it but in general those guys at Honda
, Tohatsu, Mercury
etc. are pretty smart fellahs...