Hi,
Yes, you likely need to go back in the carb. But do yourself a BIG favor and order a gasket set (item 1 in the link below). The fuel flow is highly dependent on those two little orings sealing perfectly. Use great care when removing and replacing them and use dielectric grease or Vaseline on them when reinstalling them.
First off, make sure the engine is actually running on both cylinders. The Honda twins will start and run on only one hole and can fool you. Do a power balance test by removing both plug boots and smearing some dielectric (tune-up) grease inside the tip of each one. Then reinstall. This makes them easy to remove and put back on during the test plus the grease helps seal out moisture.
Start the outboard and pull one plug wire using a DRY rag or thick gloves. Note the change in how it runs then do the other cylinder. If one of the cylinders isn't contributing at all then there will be no change when that plug wire is off.
When you have your carb apart, check the numbers on the main jet (item 22 in link) especially if you live at sea level. If someone set this outboard up for high altitude use it may have the wrong jet for your location. Sea level operation requires the largest size jet (102).
Make sure you pull the idle mixture screw (item 5) and hose out the idle passage forward and backward.... Meaning? ...Find the tiny hole on the top of the carburetor throat that is visible with the throttle plate closed. Put the straw tip of the cleaner can right up against it and seal it as best as you can. Flush that passage backwards and forwards like that. The idle passage MUST deliver fuel in all "modes" of operation and, thus, has to be clear. The new oring will ensure that the idle set screw is properly sealed so that it won't pull in air.
https://www.boats.net/catalog/honda...s-vin-babl-1200001-to-babl-1299999/carburetor
Pay particular attention to the JET SET (item 11 in the link) it feeds the passage that leads to the intermediate and high speed circuits at the top of the carburetor. The jet set has to be completely clean and also not cracked along the length of the tube. You should be able to see through the length of the tube as well as through all the drillings on the side. It has to be carefully pryed from the top of the carb throat to properly clean. The new oring will ensure proper sealing and fuel flow when carefully reinserted.
That tube feeds the passage that leads to drilled holes at the top of the carb throat that you can see when the throttle plate is held wide open. You will want to backflush each of those passages as you did with the idle orifice while you have the tube out. Spray into the hole the jet set goes to and note where the cleaner escapes. Some will come from the front of the carb through two passages located above the carb throat. Those are your high and low speed air jet feed passages. Hose them out, forward and backward, thoroughly. That's where very tiny critters take up residence.
Any time you flush a passage and see the fluid escape from more than one spot, plug one of those and then the other to get maximum cleaning. Then flush into those spots while plugging the original location and then the other escape point. This ensures thorough cleaning of these complex passages.
I'm sure I've left something out but this is a BUNCH of typing on a phone keyboard and my thumb is tired. Get back to us on what you find or questions you have about any of my rambling.
Good luck!