It depends on how far south in Florida as to whether a weeping willow would survive. Even if you're north of the survival line, that doesn't mean the tree is going to perform well or look great, which is why, I presume, you want it. When plants are planted close to the limit of their range, they may eke out a life, but not be very happy about it. If there are no weeping willows anywhere around you, it is likely that everyone before you learned that they don't do well there.

Even in climates where this tree is very well suited it tends to be problematic. Not long lived, very brittle wood prone to breakage and susceptible to countless diseases and insect pests. And with an extremely aggressive, water-seeking root system. Not at all suitable for an average suburban garden.....acreage, yes.

And if you experience the effects of hurricanes, you really want to avoid!

Visit some arboreta or public gardens in the region, see what they have - even if you see no willows you might see something else you would like to try.

Otherwise if it were me I would probably try to get one or more of these going there, local climate permitting. Notice the following discussion mentions a 'Pendens' version with weeping branches:

http://gardeningsolutions.ifas.ufl.edu/plants/trees-and-shrubs/trees/bald-cypress.html

Hi all thanks for the sobering advice. I have decided to let go of the willow tree idea and have planted a bottle brush instead. They have the same "weeping" look and will be much happier on my land.