Tingly feelings in your body are almost always nerve related. Sounds like its pressure on a specific nerve thats causing this issue for you. Hopefully nothing to be alarmed about but that you are putting a strange pressure on a specific nerve.
I bought a "switch grip" that completely fixes the tingling and cramping for me. I have the "satisfye pro" I think. It's pretty big, but there are smaller ones out there if portability is important to you
Ergonomics for me. The buttons are far too close to the edge for my big hands, and it's so thin and flat I have to grip it more with my outer-most fingers than a random comfortable controller.
Had this issue as well. I now use it as a display only and always play with a controller (tabletop mode). If I can't use a controller, I play slower games (like Civ).
Your problem is probably not the weight of the Switch, but that you're resting the weight of it and your forearms on your ulnar nerve (the "funny bone"). Next time it happens, try lifting your elbows off the couch. You'll be supporting more weight with your muscles, but I bet the tingling would go away pretty quickly.