I wish there was some sort of serial number database on there to identify an individual item.
With serial number - do you mean the number signed on the base of your weight (U5082)?
I very much doubt this ever existed - and if it did, it was discarded during liquidation in 2006. You could do some rough estimates yourself

: these production numbers were introduced in 1983 (starting with A) - and between then and 2004 the number of unlimited weights produced per year varied between 50'000 and 140'000 ... that adds up to between 1 and 2 millions of weights ... and what would be the benefit?