Younger people tend to be more creative and flexible in their thinking. As they get older those tend to diminish, but they gain knowledge and experience. I suspect that until somewhere in middle age the gains from knowledge and experience beat out their thinking becoming less flexible and creative when it comes to making well thought out political decisions.
How many times do you see articles about 18-23 year old people doing something stupid, and people come to their defense saying something along the lines of 'They're only children!'?
If you add an assumption about life experience though, You're going to have to be a lot more specific to explain how these two functions interact. why is the optimum in the middle? Why isn't it bumpy?
As soon as you start adding other factors into your weighting function, I don't know how you can be confident in the shape of your graph without being precise with your functions.
To be fair though, I think that there's a pretty good argument for inverse age weighting. If you're 20, you will eventually have to be 35, so it wouldn't make any sense for you to screw over 35 year olds. If you're 35 though, you'll never be 20 again. There is no incentive for you to not screw over 20 year olds. (unless you have kids, but at that point, everyone has equal investment in society and the premise falls apart).