I assume since weight is a concern you don't want a cast net, but if so, Cabela's has more versions than you can shake a stick at-
http://www.cabelas.com/cabelas/en/templates/index/index-display.jsp?id=cat400013

Go for the monofilament, the nylon ones tend to tear easily.

Sportsman's Guide has cheap seine nets in a bunch of sizes, but again, weighted, so may be an issue-
http://www.sportsmansguide.com/net/cb/cb.aspx?a=60479

The one mentioned above is a goodie, here's a link-
http://stores.ebay.com/FLORIDA-NETS/HOW-TO-MAKE-A-FISH-GILL-SEINE-NET.html

They may custom make what you want.............