I noticed the tent does not protect you from getting wet in rain when you sleep inside, which seems like an oversight. I think sleeping in a tent should protect you from rain.
I didn't say it was the best solution, but it's either that or haul yourself back to Silverpine each night if it rains. All you need is a pickaxe(2), hammer(2), and the tent(5), which is 9 weight total, then find some rocks to mine. Also, if you make your camp site and leave stuff their, it lightens your load. Just be sure to be back to that tile before midnight rolls over, otherwise you'll lose it all.