To the best of my knowledge Beretta has never made a to scale 28. The smallest framed box lock O/U was their AS20 series guns made thu the early 60's. It was never, to my knowledge, offered in 28ga.
You can fit 28ga. bbls., if you can find a set, to any of the BL series 20's and those same guns were offered in 28's as well, but they are hard to find for sale. Coles would be a good place to start. They helped a friend get a set of Beretta 32 ga. bbls. for one of his 6 series 20ga. O/U guns.
I think you might be able to put a 26" bbl'd BL28 that weighed within your specs together, but it would largely become a matter of the wood's density and stock & forearm configuration plus hollowing to bring it in under 6#'s. You could consider having the side ribs removed for further weight reduction, but those last few ounces often become quite expensive.
