Why the 16 inch wheels?

[kp]

I have the original size rims on my 31 coupe,the front end has been rebuilt and properly alligned,but on the paved county roads it will dive to one side or the other (hedge hop) maybe due to the narrow tires catching all the groves and uneven surfaces of the road,you really have to keep both hands on the steering wheel and pay special attention all the time,I am wondering if 16 inch tires would make a big difference in how it handles and drives .