Did you try heating the screws before attempting to remove them?
Most manufacturers use a thread locking material on small screws to keep them from working their way out. A little heat before trying to turn them will normally keep you from stripping the #heads.
Blue Locktite can usually be removed without much heat if any at all, but heat may make it much easier to get started. Red definitely requires heat.
As for tightening, if the screw is actually stripped to any degree, it's best to replace it -- or face the same stripped screw (probably in worse shape than before) when it needs removing again.
As with most things needing repair, if you have to use too much force to get something to move, you're probably doing it wrong. Before you strip a screw head, break a part, or strip the threads in a piece of plastic or soft metal, make sure you know what you're doing first.
Some things require that you destroy a small part to remove it, so make sure you have the replacement part handy before you start. Springs are especially annoying, as they can slip through your fingers and fly into another dimension, never to be seen again until you vacuum the next room.
Amazon has a TON of bit and key sets that include the "elusive" 2mm size. I'd say if a 2mm hex screw is stripping, your 2mm hex bit is plenty strong. If the bit is being damaged by an aluminum or tiny, thin steel screw head, you're probably not going to get much better results with a more durable bit. That bit will likely strip the screw slot.
Too much force = more time and money invested to remove the part and replace it. Take the time to see if heat helps. If you can get any WD40 type of liquid inside where the screw is, it's worth trying to break the part free if there's corrosion or just too tight.
If the screw is too stripped to remove with the prescribed tool, you'll need to drill it out or use another removal method. Simplest way is to use a Dremel with a cutting wheel. Cut a slot across the stuck screw to fit a small flathead screwdriver tip/bit. This works best for screws where the head is above the surface of the workpiece. Try not to let the Dremel cut into the material around the screw. This is the fastest way I've found to remove most screws with stripped heads. I always apply heat, too.