I think people pay less attention to the idea of matching the cartridge to the gun than they should.
Very small guns are best suited to .22lr or even .22 short. Even the NAA Minis require a larger, heavier frame to handle the .22 Magnum - and a larger grip change is often recommended because the magnum mini tends to jump out of the hand using the small birds-eye grips.
I recently got a S&W 351c - 7 shots of .22 magnum in an 11-oz AirLite frame (alloy cylinder). I consider this a very good match of frame and ammo. I don't think the 10-oz scandium frames in .38 Special and .357 Magnum are a good match of frame and ammo.
The AirWeight frame, which is around 15-oz, has a steel cylinder, and is about the lightest I wish to use for .38 Special - A steel J-frame at 20-oz is much nicer with .38 Special, but the K-frame platform at closer to 30-oz is an ideal match for .38 Special. The 36-oz to 40-oz L-frame is a nice match for the .357 magnum. The very heavy N-frames make even .44 magnums somewhat pleasant to shoot.
Bottom line, it usually doesn't pay to swing too far away from that ideal match of weight to power.