Is a lookup table the best option?

Given that the response appears to be linear and assuming that when weight is 0, analogread returns 0 and when weight is 1500g, you're getting 2v, we can extrapolate and calculate that a weight of 3750 will give 5v. The voltage is an irrelevance however, you can just map analogread from 0 to 1024 to 0 to 3750 to get the corresponding weight in grams.

Caveats - Does no weight actually give zero reading? Is it linear enough for the accuracy you want? Are the things you're weighing all <= 3750g?