My basement darkroom has the same issue. I have a dehumidifier running all summer. It sucks out about 1.5- 2 gallons of water from the air each day. I do turn it off while I'm working in there, as it is a bit noisy. I store my paper ( and powdered chemicals) in another part of the basement which doesn't get as humid, but I added a dehumidifier to that room before summer. You can get a decent dehumidifier for around $200.00. That's less than the value of even a small stash of paper. Additionally, if it's a severe problem, moisture can adversely affect electronic components.
A bonus I've noticed is my air conditioner doesn't seem to cycle on as much to maintain temperature.