I would quite like to get hold of a large stock pot with a thick base so I can make things like preserves as well, but whenever I look at kitchenware in my local shops (I'm in NZ if that makes a difference) the stock pots I see always have very thin bases, no thicker than the walls. Are the ones with heavier bases called something else, or am I just finding poor quality pots? 
Try searching for "laminated base pot", alternatively 'sandwich' or 'encapsulated'. Other terms tend to be more trade markey, multiclad etc. You could always buy a cheap pot & an even cheaper simmer ring instead ;)  