Sorry if somebody has alredy said this. I have the original silver alien ds and its hinge was losse and it broke although it broke four years after i got it my 3ds hinge is a bit flimsy some time if i hold it verticaly it shuts do i need to get it replaced

The top part of the 3DS is heavy, so it falls on its own weight. It's normal.

If it is really flimsy, take.it back or call nintndo.

Get some hinged armor. Like the new Zelda OOT armor for your 3DS. For your DS lite get some Nerf armor I don't have it but it's rubber coated and looks like it has good grip