Appropriate Path for Differet Size of Agent in 2D Grid Graph

I just bought A*, from this example, i would like to ask as follow:

1.How to make object move from point A to point B as shown in the picture choose path that appropriate for its size? (Big object should use big path)

2.From the picture, the big size choose the same path as small size and can squeeze through the wall. That lead to another question how to avoid mass of the object pass through obstacle?

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You can take a look at this tutorial for some options: Multiple agent types - A* Pathfinding Project