Maybe a bit more on the flop with a draw, isn't really gonna change his calling range much if at all and I doubt balance is an issue vs. this guy.
Don't think c/c (depending on sizing) is that bad (although I guess makes sense if you say it's the worst out of b/f c/f and c/c), diamonds missed and it's likelyish he will check back some better hands like AJ etc. Depends if you mean weak = fish or weak = passive/weak too.
Bet/fold smallish like you said seems ok since he will by the sounds of description fairly rarely bluff raise you, if anything this way you stop him from making a profitable bluff (since even if he bluffs sometimes, may not be enough for you to c/c). He will prob also look you up with every Ax combo he has although obviously he can have a lot of two pair now - but he won't raise them. Betsmall/fold seems good, don't know if you'll get value that often (although like I said worse Ax A6/7/8 will all call but you do lose to every other Ax, and don't think anything else worse is calling often) but it has other benefits