Yes... the wheels probably need replacing. The rims appear to be steel, which are heavy and probably not the best stopping in rain. I really like the glow on the paint... did you repaint or is that a super wax job?

As for the hi-ten frame tubing, I wouldn't worry too much about it. With lighter wheels, you will probably be under 30 pounds.

I'm rebuilding a Fuji S10-S from 1972, which has similar components and weight. Steel rims too, which I might replace.