I have heard many good user opinions of the Marlin Papoose, though I've not tried one.
I do like my stainless CZ made M6 in .22 Hornet/ .410 gage. If you get involved with the medium powered .22 H loading, you'll have to get into reloading, since factory ammo is $22 per box of 50.
The non-CZ made ones are often accused of inaccuracy. Mine does under 2" 100 yard groups(benchrested). Any rifle that shoots under 2 minute of angle is just fine in my book, for hunting.
I tried the .22 LR chambering at the same time I tried the .22 Hornet chambering ( lucky day at the range), and realized that with this weapon, the rate of fire would be so low, that I would want the most powerful loading I could get, so I bought the centerfire version.
If you want small and light, consider the various ultra-small "youth" boltactions put out by the gun companies. I really like the .22 LR Chipmunk, myself.
Good luck in your search for lightweight hunting stuff. Too bad NFA '34 killed off the Marbles' GameGetter.
Cheers