As most of the fellows have commented, this model does have a stiff rear suspension. I personally think its because of the reduced chassis weight from rear. And yes it tends to roll during high speed cornering (partially because of torsion beam design).
You can use aftermarket tyres upto 185. The front suspension behaviour goes a bit soft in that case but rear behaves the same (more or less). I have 195 installed. They do increase grip but reduce economy (in my case). So i wont advise a 195.
In a nutshell, keeping the profile same (65) and increasing the tyre width from stock 175 does increase tyre wall height (in 175/65/R15, the "65" indicates a % of 175.) and can smooth up the ride but i would say if you are not a high speed cornering junkie and dont brake at the last moment, the stock 175's are reasonable.
P.S. Whoever advises to switch to alloys for more comfy ride, has never compared an alloy rim weight to a steel rim. The higher the rim weight, the more inertia it gets when hitting a bump (even the slightest), and the more suppress action a shock absorber has to apply. And since we have already concluded that this is a stiffer suspension, by the time, a shock absorber responds, the jerk has travelled up the chassis. Only the OEM alloy rims perform reasonably good (balance of grip, stability and smooth ride). and in this case, honda did not offer them.