BAD idea with the car batteries. Acid fumes inside your house are not a good mix. If you like the idea of adding high mass low volume, go to a tire shop and buy their scrap tire weights. Better still, deck the floor with loaded ammo cans once you’ve bolted it down. You do have more than a couple boxes, right?
Another idea is to take an ordinary closet, back the door and inside walls with plywood, pin the hinge side, and a decent deadbolt. Chopping through the door or walls just gets to more resistant plywood. Put it on its own alarm circuit.
“BAD idea with the car batteries. Acid fumes inside your house are not a good mix.”
A very bad idea. In grad school the lab next door bought a $300,000 spectrometer and put it over a cabinet that was used to store bottles of sulfuric acid. Within a year all the electronics were corroded.
Acid from a dead battery is easy to neutralize.