Tire size with leveling kit?

Hey, I just bought a 2013 TRD Off-road Tacoma and I am trying to find out what the largest tire size I can run is. It came with a leveling kit, I don't know what size But i'm guess maybe 1.75"?

I found the post saying what the stock suspension tires sizes are (For 2005+ Tacomas: 265/70/17, 265/75/16 or 265/65/18, depending on what size wheels you have) but I'm wondering if the level kit will allow me to run a larger tire without rubbing. Most post I come across everyone seems to have lifts and not just a leveling kit.

Also, is there is a cretin backing spacing I need to run a larger tire? I'm going to be buying some new rims.

The current tire size is 265/70/16

Thanks for your help.

A couple pics:

 

Looks like you have ~2" up front. Show us the leaf springs and axle so we can get a better idea what's going on in the back.

You'll be able to run 265/75r16 without rubbing, which you can also do if the suspension was completely stock

 

Looks like a 3" lift via spacer(aka danger zone).

Be warned, your shock is now your bump stop.