small frame (Ie 20g frame) Beretta 68x guns can run a variety of weights depending on density of wood/etc.

I had a 687 L (no sideplates) with very nice factory wood that originally had a 20g 28" barrel that weighed 6lb 1 oz. I had Cole fit a 28g 28" tubed barrel and tune the trigger on it and it weighed 6lb 2oz with those barrels. I was able to use the same fore-end with both barrels and maintain similar handling.

The 28g 28" barrel option bacame very desirable since the 28G 26" barreled guns tended to be whippy and the extra couple ounces out front made for a very smooth handling gun.

IF you can find a European market 68X 28g gun with fixed chokes they weigh a bit less. BSA used to bring some over from UK on occasion.

Courtesy of a WOMBAT
* (Waste Of Money Brains And Talent)

YMMV