A used SKB Ithaca Quail Model (20 ga SxS) will come in at 6 lbs or less and has a single trigger. The LOP is <14" and they have 25" barrels. A Beretta 28 ga would be high on the list.

If you can live with double triggers I would look for a Webley & Scot 20 and it will be well under 6 lbs and have better handling characteristics than many other options. The 26" barrels are out of favor right now and that might be a good alternative and run a little less.