Such a metal would be good for thrusting weapons like a daggers, shivs, and rapiers; mediocre for slashing weapons like cutlasses, scimitars, katana, etc. that rely more on their weight but still use speed and a cutting edge for most of the damage; but poor for a throwing knife (poor balance, affected by wind) or any edged blunt-force weapon (like a long sword, most swords fall into this category). It would be worthless for maces, flails, or any other non-edged but metal blunt-force weapons.
On the other hand, such a metal would be wonderful for bayonets, arrow tips, spear tips, or any other application where the blade is connected to something else that represents the bulk of the mass. It would make balancing such an object much simpler and would overcome the problem of breaking under the leverage applied by the item the blade was mounted to.
Ultimately, the metal would be fabulous for door bracing, carriages, or any other construction where metal is used to support the construction but the weight is an issue. The guys using wheelbarrows and building skyscrapers will erect a statue in your honor.