Don’t know if this has been asked before but given how often lords arrange marriages on their own in this series how much power does their ruling overlord actually have to dictate such matters, both in real world history and speculated Westeros’

This is a really tricky question, because the situation seems to vary enormously. In some cases, vassals marry on their own without informing their liege lords – Rohanne Webber and Ser Eustace Osgrey, for example – and sometimes they need permission from their liege lords, and sometimes their liege lords is supposed to make the decision for them (as in the Hornwood Crisis), and sometimes their liege lord can marry them off without their consent (see Ellyn Reyne).