Obviously the thread experience load on her flanks, as it should. The load on the stem, already correctly stated, comes from valve operation. But the bronze nut is suppose to wear, that is the purpose of using the soft metal. As UncleSyd suggested, you need replace the nut.
But to answer your question, no you cannot make a generalized statement that thread stress is doubled because of the wear. First of all, wear is secular and cannot to be constant over an epoch. Second, you need to classify the thread and obtain the geometry of the profile. You can then apply the equations from ASME/ANSI B1.5 (Acme Threads), ASME/ANSI B1.8 (Stub Acme), ASME/ANSI B1.1 (UN)or ASME B1.2M (Metric) to obtain the thread area per unit length engagement. This is simply multiplied by the nut height for a numher giving you thread shear area. Knowing the material stress, you can obtain the maximum allowable stem force or figuring out the physical load experienced by the stem, then obtain the actual stress on the threads.
I think that UncleSyd is correct in assuming the thread profile to be Acme. This is fairly common in valve stem design.
Good luck with it.
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada