Just wondering:

How/when do you get more powerful weapons?

I'm lvl 9 and the most powerful one I have is the 2-handed Akaviri Dai-Katana(8).

However I usualy use a 1-handed silver longsword(7) or an enchanted silver dagger(6 + 15 shock). Takes 2-4 hits for a scamp.

I see regularly on the forum people talking about weapons with 25-ish damage.

Does it come as you level up or...?

It comes when you level up I currently have three enchanted blades, two longswords and a dagger. But at the moment I only use my Dremora Longsword that does 11 in damange I think, without any enchantments - and I'm level 11 Got it in Oblivion...

at level 10 you'll see dwarven stuff
at level 15 you'll see glass
at level 20 you'll see daedric as random loot.