Like a lot of other types of oil, there are "thick" and "thin" oil arguments for SUs.
I'm personally in the thick camp. The whole purpose of the dashpot is richen the mixture on acceleration(or as folks who've really looked at AFRs during acceleration tell me, they will always go lean, but the dashpot makes them go "less lean"). Thicker oil slows the rise of the piston, which should increase the "accelerator pump" effect of the carb. I run 20W-50 in mine, and as much as anything because that's what I'm already putting in the engine. One reputable MG mechanic I know(John Twist) swears by 90wt gear oil, which at typical carb temperatures has a viscosity similar to 20W-50 or SAE30. I've gone as high as SAE60, but didn't really see any difference and that's not easy to find.
I constantly hear of the people who use ATF, MMO, or the like having to top them up. With engine oil, I don't think I've ever had to add any unless I intentionally dumped it out.
By the way, after putting a hotter cam in my MG, I had a terrible time tuning mine. If I got it to where it was somewhere in the ballpark of correct at speed, it would be so rich at idle that it would coke up the plugs in no time. I talked to Joe Curto, one of the SU carb masters, and he sent me AAA needles for my HS4 carbs. That's considered a "richer" needle than what I had, and it's a bit counter-intuitive to think that would fix the problem but it did. They're still not perfect but they are a LOT better.