The AHA does not require the weights unless you are a Total Performance Records (TPR) breeder. Non-TPR breeders don't get EPDs on their registration papers, but can get them seperately for a fee. The customers of a TPR breeder get EPDs on their papers, and if a TPR breeder buys from a non-TPR breeder, the EPDs will appear on the new registration papers that are transferred to the TPR breeder.
The AHA registration form provides a BW spot for everybody, and most folks I know, even if they are not TPR, still report BW.
While I think it is a good idea to report all weights, and I do since I am enrolled in TPR, I don't think it should be mandatory. It just goes against the grain of a free country, and seems to me it would discourage new memberships. Some of those small breeders may get bigger some day.