32x32 sprite takes 3x3 tiles in a 16x16 cell tilemap?

Unity Engine
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I have two types of tile sprites: 16x16 ones and 32x32 ones. If I drag a 16x16 tile into a palette, and then a 32x32 one to the same palette, the tile is centered in 3x3 cells (as seen in the attached image), instead of tightly fitting into 2x2 cells. But when I drag a 32x32 tile into an empty palette, it fits snugly into a cell, even though it covers 2x2 cells in the scene grid. However, I don’t want to have to separate them into different palettes, especially since there are other sprites with different sizes.

What could be going on here and what can I do to solve this problem?

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If you want the 32x32 sprite to be 1x1 tiles then you have to change the pixels per unit of the sprite. This is how many pixels in a sprite take up 1 distance unit.

I have 16x16 sprites and I set them all to 16 pixels per unit to make them fit.

Locate your sprite in your project and in the inspector under Sprite Mode, you will see a field called pixels per unit. In your case, set it to 32 as your textures are 32x32 pixels.