I’ve always read those as scare-quotes, like the store is making fun of itself in some self-aware fashion for not being big. I know I am wrong but I would rather be wrong is a slightly funnier and less stupid world.

Also quite common in Germany. I choose to interpret them as scare quotes implying irony and smile to myself at Bob's "Big" Bookstore and the grocer selling "fresh" fish.

Even worse with food.

> Bob's "Best" Burgers

what's wrong with the burgers??

Is that for emphasis, or is that to cast doubt on the word?

Is that really common?