Thanks!
How standard dowries are in Westeros is unclear – in ASOIAF, we only have the case of Fat Walda and Roose, Lyonel Corbray and the merchant’s daughter, Myranda Royce’s potential engagement to Harry the Heir, and in WOIAF we only have Argilac Durrandon’s offer to Aegon, and Aegon IV’s payment to the Archon of Tyrosh. They seem to be used in cases where a match is being made that one party wants more than the other, and the first party is sweetening the deal to get the other side to sign on, or as a match between unequals (House Bolton being older, formerly royal, and somewhat more powerful than House Frey, Corbray marrying “into trade,” Myranda being already married and only recently belonging to a house with its own fiefdom).
If Westeros is anything like medieval Europe, however, they’re not just for the nobility. In a world where there isn’t a free market in land, marriages are how peasants can try to access economic security and social mobility, by merging neighboring farms into larger farms so that you can take advantage of economies of scale. Thus, poor peasants become middling peasants, and middling peasants can become rich peasants, and rich peasants become merchants.
A standard dowry would obviously vary by rank, but it would usually take the form of a regular yearly income or a one-time store of treasure if one’s family was flush with cash, or in the form of land if one’s family had huge tracts of…you get the idea.