Have a couple of Oblivion extremes, they are in my opinion very nice bats, though mine are literally at the extreme end of their weight range (one at 3.3 and another at 3.5). Huge bats, very powerful, they are Grade 2 willow (though I think in some shops they say Grade 1 at least on their websites). Your other options for off the shelf bats at the Maverick Colossus and Powerbow extreme from GN. They are both considerably cheaper than the Oblivions, though I think they tend to be 3lb ish or above, though when I asked around the Oblivion were usually the biggest (including the two I got).
Another option would be the Kookaburra Ultra Menace which I think would fit in that weight range are are not very expensive either. I think the new Dynadrive's also go as high as 3lb (not sure on the pricing). So a few options there apart from having one custom made. If you want Indian bats, I think the Big Ton 47 from SS goes over 3lb so that might be an option (ie they should easily have pieces around 2.12 or more). I think the SG T-20 style bats may also be around that range (Stud T-20 and T-45).