I hate to answer a post with a bunch of questions, but we can give you a better answer if we have more information.
You say it smoothes out under load. Does it run rough only at idle speed? or does it also run rough at higher RPM's with no load?
If it runs rough only at idle, would you say it is "surging"? high RPM, then low, then high again, etc.? This could be a problem with the governor. Or a vacuum leak if your engine is really sophisticated. If it just runs rough with no cycle of high/low RPM, it could be an idle screw adjustment problem.
When you had the carburetor off, did you remove the adjustment screws and squirt some carb cleaner up in there? I don't know anything about your carburetor, but it's common for them to have at least one adjustment needle screw, and sometimes two or three (one for idle mixture, one for high speed mixture and maybe another to limit the throttle closure at idle).
Post more information when you have time.