Pretty big. If you want to use LGPL Qt you need to dynamically link, so deploying will get you around 20 MB of libraries. You can do a command line JUCE app in a few hundred KB, or a GUI app in not much more.

Is the support for static linking good in JUCE, such that you can release non trivial programs in a single binary with reliance only on system libraries that are pretty much guaranteed to be there.

Yes. I only use JUCE on OS X and Windows, but it's all statically linked and looks like it should be on other platforms. On windows you can change the linker settings from /MD to /MT so you aren't even depending on the MSVC redistributables that a completely bare system might not have.

Great! It's nice to be able to easily build and distribute a single executable. Many users are barred from installing software; but can grab single file and run it.

JUCE used to have a feature where the entire library was distributed as one .cpp and one .h file. It made it very easy to distribute JUCE based source code. The make files were very simple. Unfortunately that is no longer supported.