I did some experiments years ago with my previous TR3A, and decided that straight 20 weight gave the best throttle response. Any thinner than that produced a bit of a lean bog, while 30 or 40 weight was definitely too thick and made it harder to control the engine smoothly.
But straight 20 weight is hard to find these days, so when I got the current TR3 running, I used 20W50, which worked well enough. Almost no noticeable difference when I eventually found a quart of 20 weight and went back to that.
I actually built a crude "vacuum cleaner" from an old mason jar and a cheap venturi vacuum pump from HF, just to make it easier to try different goops without removing the domes. I also eventually learned that my domes have enough slop in the mounts that just R&Ring the dome can affect jet centering! Gently twisting the dome CCW while snugging down the screws seems to make it more repeatable. (I'm sure CW would work just as well.)
PS, no doubt it depends a lot on where you have the base mixture set. If it is a bit on the rich side, then the accelerator pump effect is less important. Ambient temperature will make a difference too, both because the carbs tend to go rich with hot air and because the oil thins out when it gets hot.