AS johnross says, heat is also your enemy. I have seen a record which warped into uselessness because it sat on an English windowsill on a summer day. One day!
As Bill D says, they should be stored in their sleeves, on edge, and not allowed to lean sideways.
As WYSIWYG says, you also have to look after the sleeves, which could be the hardest part of the exercise.
The obvious part of the attic to store the weight is over or near an internal wall.
I would think carefully about putting silica gel among the LPS. Its purpose, after all, is to attract water! A plastic tarp thrown over the boxes, with the silica gel under but separate (and in a large, waterproof tray) is as near as I'd put it.
Perhaps you should talk to an archivist. They do know about preserving paper, after all.