There is a previous thread covering a problem just about identical to yours, and I suggest you read it carefully:
https://www.outdoorking-forum.com.au/forum/u...p;Words=gcv160&Search=true#Post38602

Unless your governor linkage is sticking, which is a problem I don't recall ever encountering with a Honda, you have lean mixture. This would be caused either by an intake pipe air leak, or partly clogged jets in the carburetor. The idle jet would be completely plugged, and the main jet and/or emulsifier would be somewhat obstructed. This would have happened due to dirt getting into the fuel tank, and in due course piling up in the center of the float bowl and being drawn into the main jet, then migrating from there into the emulsifier and idle jet. The idle discharge port, which the idle mixture screw partly obstructs, may be blocked as well but more likely will not, due to the tiny size of Honda's idle jet. The idle jet is drilled to 0.35 mm diameter. The main jet on your engine will be about 0.55 mm or so (I haven't measured one on a GCV160, but it is 0.55 mm on the smaller GXV140) which is 2.5 times the area, so the idle jet is far more prone to blockage from fine particles.

I suggest you proceed exactly as very busy did in the thread I have referred you to. Don't leave out any steps: check the fuel feed system and the governor mechanism before you remove the carburetor. Check for possible leakage past the gaskets on both sides of the carburetor insulator. If at that point you haven't found the problem, clean the carburetor in detail as set out in that thread, in particular the on-line videos that are referred to. Report back as you go - we'll be happy to help at any point if you just ask.

I hope you'll keep us posted as you go.