My black background problem may be more complex than I first described.
In both armor and weapon stockpile, there is only one item per tile (item + stockpile + ground, as seen in the look window). But armors have transparent background, weapons don't. The weapons in stacks near the top left corner of the weapon stockpile have transparency (you can see two items), so I think my tilesets are done correctly (I can upload them, if someone wants to check).
There is a similar problem with the block stockpile: some of the blocks with black background are alone on their tile. The block over stockpile background in the top left corner is actually stacked with several other blocks and a bin.
I think my bags are also victim of this.
There is also the same problem as Obsidian Soul, where a few tiles may have a black background depending on the position of the view, but it is more rare (the top left and bottom left blocks in the stockpile may have stockpile or black background depending on the position, other tiles don't seem to change).
