Could be a problem with your carb linkage. If you removed the carb for rebuild and then put it back on and did not re-sync that could be the issue. I ran into a similar problem with my 1963 Erude 40 after I rebuilt my carb. Quick way to tell if your out of sync is with the engine off:
1) open the front flap of the carb (the one conrtoled by the auto choke)
2) look through the carb body and observe the rear flap
3) shift your engine into forward and advance the throttle until its wide open
4) at full throttle the rear flap should be open and completely horizontal
If its not horizontal your carb linkage is out of sync and that might be your problem.
1960 Hawk III; 1963 Evinrude Big Twin 40hp; 1954 Evinrude Big Twin 25hp
There is another gremmie in some of the plastic tanks. The flat profile tanks, (and possibly others) manufactured by Scepter, have a fuel pickup tube design flaw. The pickup tube is only secured to the tank fitting by friction fit. There is no clamp to prevent it from falling down in the tank. At first, when I started having engine troubles at about the 3/4 tank level, I went looking for everything else it could be and finally, I realized that my second tank never had an issue, so I pulled the fitting on the tank in question and there was no pickup tube. It was down in the tank. I fished it out, stuck it back on with a clamp, and no more problems.
I thought that is was just an odd-ball happenstance but when my second tank failed, (at Arrowhead), I checked it and sure enough the tube was down in the bottom of the tank. I reinstalled the tube with a good radiator style clamp and now, no more problems.
So if you are running plastic tanks manufactured by Scepter, go check the tube and if there is no clamp holding it in place, put one on it.
If you are using a plastic tank there is a little screen on the pick up line in the tank pull the pick up line out a throw that screen away you can run an inline fuel filter those little screens may look like they are in good shape but are still.bad
Ironically, I experienced the same problem with a mid 50's Evinrude 35 that I recently bought from a fellow member here who's words I learned were not exactly forthright. That's another story entirely though. What I discovered, among many other problems, was that the fuel pump diaphragm was shot and there was a small vacuum leak between the cover of the pump and the body. If I were you, I'd disassemble it and inspect the diaphragm and mating surfaces.
Along the good doctor's line, I try to clean out internal carb passages in a rather "back-asswards" manner. After taking the carb apart, I wrap the bare carb body up in a white towel, plug one end as best as I can, and apply pressurized air to the other end. In theory, this should help to blow out the passages without potentially driving debris deeper into the fuel passages. The towel is there to hopefully catch anything that comes out and allows you to ID any crud that has been trapped by the towel. Sometimes you get lucky.
Do replace all the hoses under the hood with real fuel line material that is available from NAPA and use real gear driven hose clamps.