You can actually use irregularly sized sprites should you want to. It helps if you have the anchor points at a corner rather than the center... Try it on an empty tilemap - it should work there. The tiles are sorted in a particular order, from the bottom left by default. So if you paint your larger tile on the left, and paint something on the tile to the right, you'll only see the first half. You can change the tsort method in the tilemap > Settings > Sort Method.
Also, in tile properties, you can change size to increase or decrease the overlap.
Its intentional that the tilemapper doesn't stop you from painting into the adjacent tiles even though the current one has "written into" it - it is required for overlapping & isometric tiles in a tilemap.