Dual custody child

I have been paying my ex wife alimony and child support for my 11 year old son. He has decided that he wants to live with me 1/2 of the time. My ex wife agreed but does not believe she should reduce the amount of child support. She is remarried, just bought a house and is having another child. She told me she depends on my money to survive. Is this my responsibility or should I explore reducing my support? I want to do what is fair, but I think that if I have him 1/2 time I don't think it is fair to me to continue paying the full amount. Any advice you could provide would be welcome. Sincerely, Good, responsible dad in MA

That sounds like a reasonable ground to seek