Ok, I did a pub-med search and poked around and quitting tobacco is definitely associated with increased sweating, in general, and during exercise, and it can hang around quite a while.
There *were* a few case reports of people on meds that are metabolized via the same ways as *tobacco*, not *nicotine* and that can greatly increase side-effects from quitting like, one chick was taking a medication for restless legs, and she could NOT stop sweating until she reduced her dose by HALF. Wow...
I'd say that if it's only been a few weeks, I wouldn't worry too much, UNLESS you are taking meds, in which case you should consult your doctor immediately. Many doctors are going to a) not know or b) tell you since you're vaping, everything is the same, so you might want to do a search on interactions between quitting tobacco NOT vaping, and any/all medications you take, to bring with you... They're getting fairly good at identifying the pathways by which many medications are absorbed, but that doesn't mean your doc will necessarily be on top of everything.
Unless it's unbearable and as long as you aren't on any medications, I'd say wait it out a bit. Sweating in general is a common side effect of quitting, and the good news is you are flushing out those toxins. The bad news would be... having to be sweaty for awhile.
Anna