Doug,
That balloon is what is affectionately called "Fat Albert". It is housed just
south of Big Pine Key. There are two of the balloons and only one flies at a
time.
There are many stories of what the balloon is used for two of which are that it
is a weather balloon and the other, considering that the facility is surrounded
by satellite dishes, is that it is used to assist in the transmision of radio
signals to Cuba.