As a 5-generation Urban Northern California now in my 14th year in Alaska, I've transtitioned from being expert at foraging in grocery store + wild plants to being an ever more competent hunter-gatherer. My path included:
Friends and strangers giving me tips on fishing, reading a few books and trying different places at different times.
Participating in the Personal-use Fishery (for Alaskan residents only) for my 30+ salmon each year.
Having a friend with boat, a motor and local knowledge who takes my family along on fishing trips (I bring a great lunch, happily pay for all the gas, and bait more hooks and fillet more fish than anyone else (i.e. I'm the kind of guy you want on the boat).
More recently, I've been drafted on hunting trips because of my stunningly gorgeous legs. Or rather, that I can hike a lot and be a cheerful companion. After one has shot an elk, a few bears or a mess of caribou, the work really starts. Capable sherpas are very desireable and, in my experience, get the same share of fillets, burger and sausage as any hunter along.
But, to save weight?
From worst to best:
Big game. Just don't. State law and my ethics dictate that if you take any animal you use all of it and that means getting from the hunting ground to a truck and on to freeze/packing house. Shoot something? End of trip.
Waterfowl. Seems to involve sitting in cold water in cold weather with a shotgun, blind, and decoys. It would be a lot easier and lighter to bring a frozen chicken.
Small game - ground squirrels, grouse, ptarmagin, marmot(?), and ESPECIALLY "low-bush moose". A .22 pack rifle as suggested above. But have a bail out plan if unsuccessful.
*"low-bush moose" are what you bring home when unsuccessful at getting 900-pound "high-bush moose". low-bush moose are 2-3 pounds and better known as "rabbits". Alas, they are now coming off a population peak, but should peak again in 7-9 years.
Fishing, especialy if well off the road system. Char, Grayling, and of course salmon during the summer / early fall runs. I'll go for grayling and ptarmagin on Adak (1100 miles off the road system) in October, I'll let you know how it goes. The reports are anyone with a pulse should limit any day they want to. Mostly I'll be on sherpa duty for friends going for caribou (they introduced the caribou for the 6,000-airmen base and then closed the base leaving 300 people on the island. With no predators, they get shot or starve.
Wild plants - My wife and I mostly hiked yesterday on a trail (!) on the popular Kenai Peninsula (!) and were mostly hiking (!) and gathered 2 quarts of high-bush cranberries and 2 quarts of low-bush cranberries in 2 hours of hiking. 3 pounds of fresh fruit in maybe an extra 25-30 minutes. For eating fresh above (elevation or lattitude) above treeline, I like crowberries and they are on the plant for much longer.