These cards look pretty good.
Archer - There's a pin if this card is combined with things that make the opponent draw cards. I'm not sure if that's a realistic thing to worry about. I'd worry more that it's really nasty if you open with it.
The card has wording issues. What if you name Copper and I have 4 coppers?
Designer Rework - Since this is slightly better than Upgrade, my first reaction is that it should cost 3P. But probably 1P is fine since it means that nobody whiffs in the second shuffle.
You can remove the "When you play" phrasing as it is unnecessary.
Weaponsmith - A $4 cantrip trasher that only trashes treasures? I think that sounds reasonable, maybe even on the weak side. Spice Merchant is a good point of comparison. I like the +Action part because Weaponsmith is technically a splitter, but you can almost never build an engine from it.
It has a couple wording issues. It should require you to reveal your hand if you have no treasures. Also the "While this is in play" phrasing seems unnecessary.
Wet House - The consensus is that if Fugitive were a kingdom card, it would be too strong for $4 and too weak for $5. Wet House is stronger than Fugitive, so it should cost more. I think this card would slow down games a lot because it's a good addition to every deck, but is a bad defense against itself.
Inflation - Seems balanced, although not entirely exciting. It's a bit like Poacher in that it starts out good, but it gets worse when you start buying multiple cards per turn.
Road - Have you ever played Highway + Seaway games? It gets degenerate fairly quickly. I think Road might be too powerful. Sure, the potion cost slows it down, and you need at least some payoff in your deck. But once you have 5 of these you can just gain all the cards, and when you have 8 you win.
BTW, Road is the name of one of Asper's cards, and the art looks pretty similar too.