Philip thought it was fun to do that until I told him if he was going to act like a baby he would be treated like one. That meant, he would be taking two naps a day, would not be allowed to watch Thomas or the Wiggles because those were for big kids not babies. Bed time was much earlier than he wanted. He wouldn't get his favorite food of pizza for dinner because babies can't eat pizza. His food would have to be mashed. He wouldn't be able to go to the park with his friends after preschool because he'd have to come home for a nap. His favorite trains would have to go away because babies couldn't play with them. Etc. I told him this all matter-of-factly being careful to act like it wasn't a big deal to me either way.
For Philip it boiled down to the fact that he felt I was spending more time with his baby sister and if he was a baby too I'd have to spend more time with him. My husband helped so we were able to show him fairly quickly that he got to do things that his little sister didn't get to do and that if he wasn't interrupting us when we had to change a diaper, fed her or give her a bath we got done quicker which meant we had time to do fun things with him. During the baby's bath, dh would read him a book or they would play a game. When I had to feed the baby, I would set him up with something to do and remind him that once she was done we would do something together. Sometimes that was play a game, or watch a video together, or read a story. During nap times I made it a point to do something with him rather than try to clean up or get some errand done. It was hard on me more because I couldn't stand the mess but it made things better in the long run. Philip didn't feel as needy, demanding my attention all the time so soon I didn't have to spend the three hours of her nap playing trains but was able to throw in a load of laundry or do the dishes. It also helped because I got him to "help" with some of the chores (he could sort laundry with me, talk to me while I did the dishes, or help me by dusting the lower shelves of the bookshelves).