In the top right of the f3 menu it shows the memory usage. It fluctuates a lot, but I am looking at the smallest value it reaches before going up again, which I assume is when the garbage collector has just run.

To reproduce

1. Create a new world with all defaults.
2. Look at the memory usage.
3. Exit the world from the esc menu without closing minecraft. Load the world again. Repeat a lot of times.
4. Wait until the lowest value stabilizes.
5. Look at the memory usage.

Result
The memory usage increased from 23% when I first opened the world to 42% after having opened the world 50 times. I had given minecraft 4GB ram so I guess that means every time the world is reloaded the memory usage increases by around 80 MB. In the heavily modded world where I first noticed this the difference seems to be much bigger though, enough that the game crashed without me even trying, so it can probably be a big problem in some circumstances.

Versions
Magic Feathers: 4.2.0
CookieCore: 4.0.1
Minecraft: 1.18.2
Forge: 14.23.5.2855