I'm lvl 50 now. It's not hard to guess that there is no enemy in game anymore that can actually hurt me. But I was wondering how does my base damage grow with my level. Will I see a huge change if I hit level 70 or even 80 or maybe the damage is only based on the perks I have bought. The reason why I ask this is that I would want to level up few more things, Light Armor, Archery maybe even Sneak but I'm afraid that I'll become even more overpowered than I am now.

Your damage isn't determined by your level. Your damage is determined by your weapon, skill in that weapon, enemy's defenses, etc. Skyrim works on a level scaling system, so depending on what skills you level up with, the game can make you either stronger or weaker.

For example, let's look at these scenarios:

Scenario 1

Nord Level 10, Assume all skills are at level 25 each. (Just assume, it obviously wouldn't actually be this way)

He levels his speech skill, lockpicking skill, and pickpocket skill a few times each. He finds himself now at Level 14.

Those were all non-combat skills, which in no way, shape, or form helped his damage output whatsoever. He's level 14 now, but his damage output is exactly the same as it was at level 10. But the enemies he's fighting now have more health, more armor rating, and deal more damage, essentially making him weaker in a technical sense.

Scenario 2

Nord Level 10, again assume all his skills are at 25 each.

He levels his one-handed skill and heavy armor skill multiple times each, and hits level 14.

The enemies he's facing have more health, have more armor rating, and deal more damage than the ones at level 10. But you also deal more damage than you did at level 10, and have more armor rating etc. There's now a good chance you've either scaled well enough with the enemies to balance out, or potentially have become stronger than them depending.

Edit: Things like Smithing, Enchanting, etc can you make ridiculously overpowered, which is probably why you're feeling the way you do, btw.

An improved daedric weapon (hell, even steel weapon) can probably one shot most anything with the right professions even on master difficulty.

Great! This means I should level up some of the skills I mentioned w/o a problem. Should probably put points in Stamina not Health.