A tile layer can only contain one tile in each cell. Think of tile layers as containing not the tile pixel data, but just a tile ID, telling it which tile’s data to display in each cell.
If you want some tiles to overlap others, you’ll need to use multiple tile layers.
Unfortunately, current Aseprite has a separate tileset per layer, so you’ll have to copy/move the overlapping tiles to the new layer. AFAIK it’s planned to be able to reuse tilesets across layers.