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I don't know the exact weight, but it will take four guys, one at each corner, to handle it. It works even better if you can get two more guys, one at each wheel well. You won't want to just set it down. Set up cinder blocks and 4x4 posts or a good set of saw horses to place it on to keep it off the floor.
I moved a '64 long bed last weekend. My guess, 500lbs, maybe a little less. We had 5 guys for part of the move and 4 for the rest. It's a bugger, but we had to move it a long way! We took everything off the bed first to make it lighter.
I'd say no more than 300 pounds, I have moved them by my self, and loaded them with one other person. Four people would make it a lot easier to handle though. Can you remove it inside of your storage area? Stand it on the cab end with something under it. It takes up less space that way. I usually use 2X4s under one when I do that.
Thanks for the suggestions all, Once I get the dang four banger out of the garage it's time to do some real work on the truck! I'm thinking the rear brakes will be upgraded as it seems pretty easy to do, as well as a through and through cleaning of everything. Also will be installing disc brakes on the front! Lots of questions to come.....