I've got the 629-4 version of that gun, it's the PC Light Hunter. Mine hasn't got the cut outs for the bbl weights, but otherwise pretty much the same.
Oh, mine has sights, too....
ETA, just looked up some info I had gotten from Lew Horton, mine was one of theirs and was called the "Hunter III".
You can email Horton to see if they did yours, email@example.com