I am putting a topper (snug top) on the bed of my truck and want it to be weatherproof. I want to put a bed and a sink back there, but not have a camper. What is the best way to weatherproof the bed of the truck so I can put carpet down??

 

I would start by sealing the drains at the front of the bed and going to Home Depot and/or the junkyard and creating a makeshift seal around the tailgate.
How much you charge for rent?

 

Naturally you want to put "cap tape" around the cap. You wont get rain in the tail gate but dust sure comes in. As mentioned above a look around the home center will reveal some weather stripping that should work. A word of caution I and my hunting buddy almost suffocated in a camper that I had worked very hard sealing up. When I woke up panting you couldnt light a lighter for lack of oxygen.

 

I didn't even think of the lack of oxygen thing, good point.

OP, I would hire this dude ^^ to seal your truck cap Air tight seal!

 

I would think adding a under the rail plastic bed liner would give some insulation from the outer bed area... I would be cautious about using any spray foam insulation as it could lead to possible rust.
Maybe some thin polystyrene under the liner and on the sides...