Limit the water an hour or so near his bedtime. However as Cooper is just 6 weeks old I will not let him gulp down too much water at once. In fact it would not be amiss if you can just call your vet and take his advice.
I had my Buddy at 6 weeks too (his mother had come down with an infection and the pups had to be separated from her) and our vet had told us to keep water available at all times but not more than few sips worth at once. Good luck with the little guy and do post some pics soon.
Rule of thumb is 1 oz per lb of body weight per day for grown dogs (outside of extreme heat or exercise circumstances). I've never come accross numbers specific to puppies.
I would weigh Cooper (use a regular bathroom scale, step on it without him then back with him and take two measures at least to have a reliable one) and measure his water accordingly. Water intake also depends on wether you feed all dry, dry with water, all canned or a combination thereof. Drinking too much too fast -especially if the water is very cold- can lead to throw up.
Unless his water consumption goes thru the roof (let's say 3 times as much as what I described above), I would not worry too much. I'd rather have a pup drink a bit more and stay well hydrated than a bit less. I never restricted access to water, even when mine were pups.