Is there some ratio to it or is "1Lb off the frame 1Lb off your body"

I used to ride a bike that was about 23lb and I weighed 180lb. Total weight: 202lb.
Now I am on a bike thats about 35lb but I only weigh about 160lb. Total weight: 195lb.
I am only 7lb lighter now on the heavier bike than I was heavier on the lighter bike (sounds like nonsense but might be right) but on hill climbs is there any more advantage to the bike (disregarding wheels) being light as opposed to you?
This is without the complication that if you're thinner you're probably fitter and thus more capable anyway so will find it easier.