OJS: I like your spunk. I made sure to read your post twice so I didn't ask questions you already answered. That said, what is the make/model/year of your bike. Whether it is alloy or carbon, cartridge or press-fit and its age makes a difference.
OK, You describe it as a click, not a creak nor a sensation of popping. There appears to be no feeling of a pop in the pedal stroke from what you say. It happens near maximum torque on the drivetrain. I have a couple of ideas.
You mentioned that it goes away in the rain. I love riding in the rain, and there is one thing that will kill a pedal quickly, is rain. You also mentioned that the noise goes away in the rain. Perhaps there is water intrusion into the pedal spindle/bearing and it has caused some displacement and degradation of the grease. Rain comes, and it acts as a lubricant for a short time, getting rid of your creak. If you have another known good set of pedals, swap them out. If you don't, spray a little WD-40 into the spindle area and see what happens. You can regrease most pedals, some are easier than others. My money goes here.
Cleats will occasionally creak against the pedal itself, and I have had one make a click/creak combo. Make sure your cleats are spotless, as are the pedals and give it a whirl. There is cleat lube, but you can rub an old candle on the cleat/pedal surface if you have one. Kinda doubt this one though.
Re-reinstall the pedal, but with this time use plumber's/teflon wrap over the pedal bolt. It will act to fill any void areas, and prevents squeaking and seizing over time. Same as above on probability.
Sounds obvious, but take the rear wheel off, add the tiniest amount of lube to the dropouts, reinstall and ride. I've had what I swore were bad BB turn out to be a rear wheel grinding away at the drops during high torque.
If it is a BB, it will only increase over time. You aren't feeling any pop so it is an irritant at this point. From what has been said, I would be slightly surprised if this was the problem. Please let us know the year, make, model and BB type. That will help immensely.