OK - your really asking 2 problems
Strength to weight
and
Strength to cross sectional area
Your going to find some "interesting" thing out. For instance, Titanium, which has an amazing strength to weight, isn't all that good in cross sectional strength. In other words, if you compare it to steel wire the same diameter, it'll be weaker, but MUCH lighter. If you increase it's diameter so that it's the same weight, it'll be a lot stronger
So - based on your last message you want
1)High strenght/weight
2)High cross sectional area
3)Good abreasion resistance
4)Good heat resistance
5)Good working properties
Don't we all wish we could find such a product. Your going to have to make a tradeoff. For instance, usually 1 and 5 are upposed to each other.
As some said, the best stengnth/weight and density numbers are usually in the aramid class fibers, but they they are horrid in heat resistance, are non conductive, have problems with abresion resistacne, and self notching (kevlar is very good at cutting itslf - you have to use special knots)