... sound batting and/or weighting speakers ...

To whom it may concern; I mean no disdain in my comments. Here's the deal; I spend a LOT of time around here watching people recommend spending money on upgrades. As if money grows on trees. Sure, big improvements can be had.... if you have big money to spend AND the time and inclination and ability to shop and compare. Even then however economic profit considerations will always limit design leaving lots of areas of improvement. These can be found all over the place, from speaker gaskets that seal but don't control vibrations to diodes and caps that are cheap and hold back performance. Because of all this the spectrum of performance manufacturers leave on the table is HUGE! There are many, many significant performance improvements that can be attained at little cost. The legs of the ladder are endless. 

So, keep reaching! Make a change! Go for not just one tweak, but many, for a far superior sound. :)

At the very least I guess you can look at this as a learning opportunity. You are right, if the whole speaker cabinet is moving that is dissipating energy you want coming out of the driver. So its robbing you of dynamics. Also if the speaker wasn't so loud you could hear the sound coming from the cabinet itself, which is smearing and robbing you of detail. This is why all the very best speakers are so thick, solid, and massive. Ideally you want no vibration anywhere at all except from the driver. 

You can try several blobs of Blue Tack to hold the speakers in place. Or BDR Cones which are another better form of vibration control. Either way yes lead shot in a bag will add mass. Lead shot in a bag however is more damping than controlling. Only way to know is to try and hear how it sounds. This is why all these tweaks should be considered learning. Which is a great thing to do in its own right, especially if you keep it cheap, simple, and reversible.