What is the difference between thickness and heavy stones?
You know your stones are thick when they form a safe group that secures some territory and/or build some influence, threatens to attack... or just give you some kind of advantage.

There is no official definition for "heavy stones", but I think the term was used instead of the term bad shape for a group of 5 stones or more.

In any case, if you have a group of stones all connected together that doesn't do much to secure some territory or reduce the opponent's, then you probably have a bad, heavy, over concentrated shape.

-----EDIT-----

To add to my answer, I found some good definitions and examples of heavy vs overconcentrated and heavy which might be useful to you.