Here is a "for what is worth" type of quasi science experience/ just some more N=1 data.
Recently took a hickory bow, with sinew and rawhide backing, out to New Mexico, near Taos. Sangre de Christo Mountains. Finish is coat of tung oil, and TB3 under thin rawhide. Bow finished in Tucson May and June, RH around 6-13%.
Also, I took a bow scale and tiller stick.
Rain every day but one, majority cloudy every day; higher RH, 70% at times I guess, higher even with rainfall, and I found the bow lost around a pound. (initially, it weighs in heavier than after a few pulls or shots, so I think that shooting affects it more than the RH, at least in this scenario of leaving it in the car, five days out there in mountains). Some bouts of rain along the subsequent Chama River camp, but also that is average 31% or so RH, in monsoon season. No big draw weight loss there either.