Just a few things that I hope someone can clarify.
What does it mean when an aircraft is designated as "heavy".
It is used to indicate a number of things. First off, 'heavy' indicates that the weight of the aircraft exceeds 255,000lbs. Those that do are B753s, B767s, B747s, B777s, B787s A330s, A340s, A350s, A380s, DC10s, L1011s, B2s, B707s, Antonov 25s (I believe that's the bird), and Concordes.
Secondly, this also means that the above planes generate a great amount of wake turbulence to those within its class, as well as smaller class aircraft (B737/A320 and below). Technically speaking, a B752 generates this as well, but does not exceed the 255,000lb weight limit.
When an ATC asks an aircraft to climb at a "good rate", what does that mean?
When an aircraft climbs, it is climbing at a particular rate of speed. Standard rate for climbs and descents is 1500ft per minute. When ATC asks for a good rate of speed, they are looking for a good rate that the pilots can get the plane to the altitude assigned without compromising the safety of the aircraft. If a plane could do 3000ft per minute, and do it safely, there's a good rate of speed for the climb.
 unless configured to be so, by request. Reference the B752s that ATA uses. They are configured to exceed that limit by request. So all of their B752s are deemed 'heavy'.