Re: 1989 merc 140 h.p. I/O stalls when slowly accelerating......
When you cleaned and rebuilt the carb did you replace the accelerator pump CHECK VALVE?
A slightly leaky check valve will still seal enough to get somewhat of a pump shot with full throttle opening, BUT, small increases may not have enough volume to overcome the check valve leaking back into the float bowl.
Simple test, with the engine OFF. Remove the falsh suppressor and while looking directly into the carb watching the accel pump nozzle have a helper make small throttle increases or disconnect the throttle cable so you can open the throttle manually. Can you see a very small squirt from each nozzle? Try a larger throttle movement.
If no accel pump discharge on the small movements then R&R the carb again to clean that check valve ball and seat.