Help swallowing this bitter pill, being a child support payer.

We have 50/50 custody. I make $62,000 , she makes $42,000. The suggested child support payment is around $850/month. It equalizes our income so that we both make $50,000 per year.

People say it's for things like new shoes and clothes for the kid but that only costs at most $500 per year.

People say it's for child's healthcare, but at my income level the kid qualifies for good free healthcare because of my veteran's benefits.

People say it's for extra curriculars, but we're members of the YMCA and for membership and classes we've always spent about $150 a month.

People say it's so that the lower earning spouse can have equal housing. She lives in a big rented house with another single mom and she pays about $800 a month for rent and utilities.

Maybe it's groceries? Since she left me 6 months ago she has spent $732 total on groceries.

I know these are correct expense amounts because we still share our bank accounts and I was the primary caretaker of the kid for the last 3 years while the ex worked full time. As a homemaker I made about $30,000 per year, but we were living good with our modest lifestyle.

She leaves me and I go to get a job and now I make more than her for the last 13 weeks.

Half of all those expenses are $862. Should I really be paying half her rent and half her grocery bill?

Am I missing some big expenses that are for my kid? Doesn't $850/month seem high when you look at the real expenses? She just gets 16.7% of my income now? Please help me swallow this bitter pill.

Update: Thanks for the engaging discussion and advice. I hired a new lawyer today and she tells me that the correct amount of child support is around $400 per month. Hopefully this lawyer is correct. Always get a 2nd opinion.