Teardrops n Tiny Travel Trailers

My suburban has a 2x2 receiver hitch but my new Silverado 2500 has a larger ,2-1/2" x 2-1/2" - Class V Hitches I haven't looked but do they make a larger hitch so that it fits tight like the other one I have
One reason I am asking is when I bought my new toyhauler he gave me a huge load lever hitch with anti sway bars and it also looks like it fits the 2x2 receiver hitch.
I can't imagine that you would use a 2x2 hitch in a 2.1/2x2.1/2 receiver or would you ? do they make a sleeve or adapter to use?
My 7x16 and my open back trailer is all I have ever towed, so this is new one for me?

There sure is an adapter: http://www.etrailer.com/Hitch-Accessories/Draw-Tite/58102.html

Thanks I though there had to be something like this but I wasn't sure.

You can check at about any place that sells hitches or reciever parts.

Earnest