How deep is the overhang? All stone requires support.

It would probably be best. There are all sorts of ways to support it. Since it's going to be used for dining and people sometimes lean on the bar or use it to help get themselves up from a chair I would think about support for it especially if it is over 8-10 inches in depth and over 24 inches wide.

For me anything more than 12 inches deep should have support.
Safer that way.

What does your fabricator say?

Here are some ideas of how to support.

I'm for making it strong any way possible. You just know that somebody's gonna stand on that overhang.

"How deep is the overhang? All stone requires support."

It depends on how thick the stone is, what type of stone it is, and how much overhang is preset.

3 cm granite goes over 24 inch wide dishwashers with no intermediate support (the free span is form cabinet to cabinet) and can easily overhang 8-10 inches in most types of stone with no additional support.

Thiner granite requires at least plywood under it everywhere.

Thanks for all of the responses! Big thanks to boxerpups for all of the images (one of which we are using!). I am definitely adding support for the overhang... especially after someone gave me a visual of one of my kids standing on the counter! The risk of breaking the marble is too great considering the precautionary support is an easy and inexpensive addition.