weight has not much to do with suspension. Drive an old american car (caprice etc), those cars are damn heavy but still very unstable. it depends on the kind of suspension setup.
while the new city is reasonably stable if u compare it to other local cars of today, its true that its not even nearly as stable as the 1997-2003 shape. the reason is that the 1st gen city was much lower in height then the current city. this kind of proportions did make it more stable but it wasnt much roomy and not as comfortable as the newer ones. the focus in newer cars is on fuel economy and minimizing manufacturing costs. u must ve noticed that city 2003 onwards dont have rear independent suspension while the 97-03 model does have it! reason to stop making independent suspension = reducing cost, increasing trunk space (hence huge trunks in city 03 onwards), reduce components in the suspension and hence reduce replacement cost and increase life of those parts (as they are now simpler)
while city is reasonably stable for the speeds its meant to be driven (i ve driven it to 185km/h on stock tires and was just fine) if u still want more, get wider tires, 195 or so. may be put a few mm side spacers on the hubs to increase the width of wheelbase (although im not 100% sure if this will work or not)