Sometimes you can get a multi-kid discount - at day care, at activities like gymnastics, etc. Sometimes you can't.
I don't think kid2 doubled our expenses. Even though our kids were different genders, we reused most of the baby stuff. Ours were 3.5 years apart, so by the time kid2 needed something, kid1 had probably outgrown it. Kid1 literally got out of diapers the week kid2 came home from the hospital, which saved us $$$. And kid1 started school when kid2 was still a toddler, so the daycare expenses were only astronomical for two years.
Now that they are in elementary/middle school, the main expenses are food, clothes, and activities/school fees. Kid1 is in an expensive sport and is picky about what she wears; kid2 is in cheap activities and doesn't care what he wears. He's waaaay less expensive than she is, but even at 9 years old, he eats more.