seldom used term.
A "light weight application" is more a
thin client[
^].
A "heavy weight application" is more often used
rich client[
^].
Basically it comes to a thin client being a GUI without a background, no data storage and not much calculation going on. Most of that is made by a server instead.
A rich client is more independent, might run without constant server interaction and can do several things without asking the server (e.g. creating print outs).