[big]

BaSO₄ is a slightly soluble salt in water. But when added to a 1.0 M solution of HNO₃, though, it supposedly doesn’t become more soluble. I realize that H₂SO₄ is a strong acid, and that strong acids tend to dissociate anyways. However, HSO₄^- is a weak acid, so couldn’t that technically want to form, and while BaSO₄ is definitely not going to be as soluble as something like BaCO₃ in HNO₃, why isn’t it at least a little bit more soluble?

[Borek]

It should dissolve a little bit in the presence of strong acids. More in HCl than HNO₃, as the latter is relatively weak amongst strong acids. Evaluating solubility in - say - 1M HCl makes an interesting ionic equilibrium problem, but the difference is probably neglectable for most practical purposes. It won't be when analyzing traces.