With regards to your second question, I have the following answer:
The terminology of "heavy" you got exactly right. It's telling the controller that they have a heavy weight, meaning the plane itself is heavy, despite its baggage or people. It's more to do with the size of the plane.
I'm glad I could help.
Chananya
You're close on this one!
It actually has to do with the MTOW (Maximum Take Off Weight) of the plane. If the MTOW exceeds 255,000lbs, it is deemed a heavy aircraft. The B757-200 is the exception, as its MTOW is exactly 255,000lbs.* The B757-300 exceeds that, so it and anything with a heavier MTOW (A34x, A33x, B76x, B74x, B76x, B77x, A380, DC10, L1011, MD11, etc.) will have heavy in its callsign.
BL.
* The now-defunct ATA airlines explicitly configured their B757-200s to exceed that weight, so theirs used heavy in their callsign regardless.