Let me make a couple of comments from the perspective of my Ceramic Engineering degrees:
First and foremost, Kudos! Throwing pottery is not the easiest thing in the world to master.
There are four things that can effect the”weepability” - the clay used, the wall thickness, the firing, and the glazing.
I know it adds a new level of difficulty, but if you fire it unglazed, you can get an assessment of the first three’s combined impact, and if you can really baby it on a refire, using a lower melting glaze, you can use that to partially obscure the surface to reduce it a bit.