Suppose the process of manufacturing the armor produces a material that is lightweight and indestructible. It cannot even be dented. Suppose further that the process can be modified so that the finished product is of any size and shape we want, within reason.

I'll call this material "unobtainium."

To counter the question, why wouldn't people make weapons of unobtainium in order to overcome the armor, the response is: how would that work?

Imagine we fired a twenty-first-century anti-tank round at a soldier armored in unobtainium, and suppose the soldier is well enough braced (e.g. against a wall) so that the impact of the round does not just knock him over. What happens?

The round cannot pierce or deform the armor. It strikes the armor with great force, but the armor pushes back (Newton's laws). The reaction force may deform the anti-tank round (in fact I think it almost surely will do so) or cause it to bounce back, or both.

Now put a full jacket of unobtainium around a similar anti-tank round and fire it at the same armored soldier. What happens?

I claim that the round still exerts force on the armor and the armor still pushes back with an equal and opposite force. The difference is that this time, the unobtainium jacket prevents the anti-tank round from deforming. But it does not prevent it from bouncing off, which I believe is exactly what it would do.

An unobtainium-jacketed anti-tank round would indeed be useful as a weapon against twenty-first-century tanks: their armor is not nearly as tough as unobtainium, so a round fired with sufficient force is sure to penetrate. But if nobody is using twenty-first-century tanks in your world, the ability to pierce that armor is not worth anything.

In fact, the main thing stopping you from shooting a projectile through unobtainium armor is not the strength of your projectile, it's the inability to put enough energy and momentum into any projectile in order to overcome the armor's incredible strength. (Non-projectile weapons are even worse; the amount of energy and momentum you can put into a sword by swinging it is very limited.)

So to fight unobtainium-armored soldiers, you need to get around the armor, or find something (a force-field "blade" perhaps) that can disrupt whatever material properties give unobtainium its strength; you could shoot something at a walking soldier with enough momentum to knock him over or at least slow him down, or simply hit the armor with something that imparts so much momentum to the soldier that his bones and/or organs are injured by the acceleration, killing or disabling him. None of this suggests that these weapons would be made from unobtainium.

Warning: extreme physics-geek talk below this line.

Delving into the physics a little deeper, the force on the anti-tank round has to be exerted through some distance in order to reverse the direction of the round. Since the force occurs only when the unobtainium jacket touches the unobtainium armor, and neither of these can deform, how can the force act through a distance? I suppose that when we say unobtainium cannot be deformed, we mean it cannot be deformed on a macroscopic scale (anything you could measure with a ruler or even a micrometer); but it still consists of atomic nuclei and some kind of cloud of electrons, and as these components of the jacket approach these components of the armor, there is an electric repulsive force that becomes significant only when the gap between the objects is not much more than the distance between the nuclei, and that it rapidly increases as the objects approach nearer. This rapidly-increasing force provides the "springiness" that allows two colliding pieces of unobtainium to bounce off each other.