The weight of the diaphragm is irrelevant (or so slightly relevant as to be irrelevant).

There could be one of a couple things happening. The most probable one, if you've not already addressed it, is related to the carb diaphragm. It's possible that the airflow past the carb is interfering with the metering diaphragm's operation. One of the carb diaphragm cover plates has a small breather hole in it. This is to provide static atmospheric pressure on the metering diaphragm. Airflow can change the pressure it sees, which will change the mixture. Many people solder a bit of brass tubing onto this hole, and route a fuel line into the fuse to allow it to sense in a stable air mass.

Could also be that the cowl and airflow are causing a ram air effect on the carb intake, this can cause mixture problems. This is likely if the problem goes away when flying without the cowl.... It can then be rectified with clever baffling and venting...

Good luck,

J