Which "Sweet 16" are you talking about? The original John Browning design or the new abomination under that name? If the former then there aren't many options as the old A-5s tend to run $450-$800 depending on condition, features, and seller. The "new" A-5 is not something I am interested in and have had only a very cursory look at. The only other semi-autos I am familiar with are the Remington Model 11 (a version of the A-5), the Remington 1100, and the Winchester 1400. Other than maybe the 1100 they should run less than a comparable A-5. The Winchester and 1100 were built on 12 ga frames so would be roughly the weight of a 12 ga and the M-11 is virtually indistinguishable from the A-5.

There are mighty few 16 ga O/Us and I can't think of an O/U I would recommend that regularly falls in that price range. I have a Citori that I picked up back in 1987 and there have been a dearth of options other than that. Baikal had one I believe but they were pretty rough. Huglu/CZ might have also had one but I'm not sure. One might find one of these on the used rack but I don't think much of them.

Your buddy's options are pretty limited in 16 ga and are even more limited if restricted to just semiautos and O/Us.