Paul Farquhar
Legend
Since traveller's clothes clearly would include a weatherproof cloak, and common clothes don't, the cost of a cloak is obviously 15 sp, and it's weight is 1lb.PHB page 150:
Clothes, common 5 sp, 3 lb
Clothes, costume 5 gp, 4 lb
Clothes, fine 15 gp, 6 lb
Clothes, traveler's 2 gp, 4 lb
...
Robes 1 gp, 4 lb
Also, on page 157, in the Trade Goods section you can find that 1 square yard of linen costs 5 gp and 1 square yard of silk costs 10 gp.
I know it's not specifically a cloak, but I think you can made do with this info.
But NPCs always see the PCs coming, and will try to gouge them for whatever they think the can get, so it wouldn't be uncommon for them to ask for 10gp in my game.
Really, who keeps track of how much the player's clothes weigh?!!
Need a rule: if it is raining double the weight of the PCs clothes. Because clearly there can never be too much simulation!