The real issues with bike weight vs. rider weight is that it is really hard for a rider to lose 20 lbs .... but impossible to lose 20 lbs off most bikes. It is even harder to lose 50 lbs, and harder still to keep the weight off ...

It is really, really expensive to take five pounds off most decent road bikes ... and most decent road bikes couldn't get much more than five pounds lighter .... pretty soon you are talking $1200 wheels, $700 gruppo, $500 cockpit, $2000 frame ....

On the other hand, if I could just escape the tyranny of weak will, bad health, injury, and laziness I could get down to my old riding weight for no cash at all.

If the wife is willing to ride, and wants to lose the weight, she will for sure benefit in far more ways than she would benefit from a lighter bike.

Also, after she is svelte and fit, she might start wanting a better bike.

Let nature take its course.