<<They should aid slightly when climbing up an incline but should not help when climbing something vertical like a tree or structure.
The climbing system does not differentiate this rigorously. In fact, some parts of it are still broken and accounting for things like racial height and other randomness. Dev Team has said fixing it to be standardized across the board will happen eventually, but it's not a priority. I imagine granting a weapon type a bonus to climbing falls somewhere far behind that in priority.
