To answer your second question first, thin is the way to go. The problem is, the thinner the blade, the less rigid and strong it will be. Imagine chopping at something with a razor blade...
Blades that will cut through anything are fairly common in science fiction, and they always involve some kind of "rubber science." Larry Niven had two variations on the theme back in the 70's. One involved the invention of a cable that was a single molecule, like a flexible crystal. Since it was one molecule, it was as thin as ANYTHING could be. Since the whole "rope" was one molecule, with inter-molecular bonds (about as strong a bond as there is outside of an atom) in an unbroken series the whole length, Sinclair molecule chain was the ultimate in strength and thin-ness.
The stuff was made for (and mostly used for) tow cables, etc. But imagine what a garrote made of the stuff would do. One molecule thick, and if you pull on it with enough force, whatever it's touching will ALWAYS give first.
The other variation he used was an alien technology that involved a force field that stopped time inside its influence. Mostly used as the ultimate suspended animation, but one of the more alien gadgets was the "variable sword"--the thinnest conductive wire possible, on a reel so you could vary the length, from scalpel to claymore and beyond--with the conductive surface acting as an antenna for a stasis field.
The "blade" was completely indestructible--nothing can break in zero time. And it was almost as thin as a Sinclair molecule chain. Ugly weapon.
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With real weapons, you go for the lightest, thinnest blade that won't break, bend, or flatten when you hit your target. Then you add a little bit of weight to maximize momentum when you're chopping--or add leverage (thus polearms) or both.
Most of the magic swords in real legends were "magical" because they were TOUGH. Roland's sword was called Durendal, and it's generally agreed that the word probably came from the same root as "endurance," "durable," etc. Excalibur, according to Wikipedia, is derived from a word that translates roughly as "hard cleft," and many of the derivative writers claimed it actually meant something like "cut steel."
In The Doomfarers of Coramonde, the hero finds a sword in an armory where it's been forgotten for generations--apparently because it wasn't spectacular enough in a world with flaming swords, etc. It's a fairly ordinary looking sabre that looks like downright cheap metal. A name seems to have been carved on the blade some time after it was made: BAR.
Turns out, he eventually learns, it's real name is NEVER-BLUNTED. No matter what you hit with it, or how hard, it never breaks and never loses its edge. Nothing spectacular, but nasty.
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If you want your superhuman to be a standard "Conan-clone," then the heavy sharp piece of steel will do, with magical backing. If you want to make him exotically nasty, you might consider something like a bill or glaive or naginata--a long, unbreakable shaft to give him lots of leverage (pretty good substitute for mass, if you do it right), with a paper-thin indestructible blade on the end. Incredibly sharp, unbreakable, and the length of the shaft would let him use his strength when he needed to. But the weapon would be so light (especially for him) that it could be incredibly fast, too. Just a thought.
