Actually, I use anonymous method in Delphi and I haven't noticed nor I heard that it results in significant exe size increment.
Do you have a lot of anonymous methods with similar body?
Anonymous methods generate some code yes. For each afaik an interface is defined, plus code to move the captured state to the interface. But that is normal overhead, like adding a small class and one or two methods with say an automated type as parameter. Nothing extreme.
The extended RTTI is really a totally different magnitude, and to a lesser degree also generics (afaik though, Delphi doesn't really try to optimize generics(*), so the implementation is actually worse than the design).
(*) Delphi generics contrary to the earlier FPC and C++ ones follows a strict declare before use principle. This makes it much easier to share implementations for cases that only differ in typing. Exploiting this properly is probably a global optimization of which Delphi has few.