You don't need to weight the groups, since everyone experiences all ages (not counting early death).

My proposal is: Multiply the number of house reps and senators by ten (for instance). Each representative now represents a district / state as well as a decade of life (for instance). When voting for an age-graded role, your vote only counts towards the decade of life that you're currently in. You can only run for a position that matches your age range.

This would have a number of advantages: Disrupt two-party dynamics. Increase granularity of representation. It's harder for older folks to take younger folks hostage. Younger folks will feel more enthusiastic about voting for someone who actually represents them.

Probably, you'd want to fiddle with the numbers based on age demographics. 7-year intervals is probably the right number, with a big bucket for people over a certain age. (So, 18, 25, 32, 39, 46, 53, 60, 67, 74+) might be right.