Do you know what sets it off? Seems like it wouldn't be from impact as these balloon materials couldn't be comparable to say hitting another plane, right?
All modern missiles use a proximity fuse that selects the optimum position relative to the target to detonate, it isn't based on contact. One thing to consider is that the warhead is not in the nose -- that is where the sensors are -- but further back on the missile. These warheads often us an annular (ring-like) blast pattern, hence why positioning and orientation relative to the target at detonation time is important to maximize damage.
Adding to janderwogs response, air intercept missiles don't really deal damage with the explosion. The missiles are built with shrapnel payloads propelled by the explosion. These are what actually damage the aircraft on the receiving end.
A little research on the Canadian Ballon shootdown a number of years back show that isn't exactly the case. A larger balloon was shot with a (20mm I believe) cannon and continued to float a long distance.
‘Duds’ is an odd way of putting it. Sidewinders usually have an ‘exploding ring of metal rod’ warhead, I believe - and that was replaced by something else better suited to destroying the balloon while leaving the payload intact enough for technical analysis.
