Function objects do in fact take up a lot of space. Objects themselves may not take up much room as shown below but Function objects seem to take up considerably more. In order to test this, I used Function("return 2;")
in order to create an array of anonymous functions.
The result was as implied by the OP. That these do in fact take up space.
Created

100,000 of these Function()
's created caused 75.4 MB to be used, from 0. I ran this test in a more controlled environment. This conversion is a little more obvious, where it indicates that each function object is going to consume 754 bytes. And these are empty. Larger function objects may surpass 1kb which will become significant very quickly. Spinning up the 75MB was non trivial on the client, and caused a near 4 second lock of the UI.
Here is the script I used to create the function objects:
fs = [];
for(var i = 0; i < 100000; i++ ){
fs.push(Function("return 2;"));
}
Calling these functions also affects memory levels. Calling the functions added an additional 34MB of memory use.
Called

This is what I used to call them:
for( var i = 0; i < fs.length; i++ ){
for( var a = 0; a < 1000; a++ ){
fs[i]();
}
}
Using jsfiddle in edit mode is hard to get accurate results, I would suggest embedding it.
Embedded jsFiddle Demo
These statements are incorrect, I left them to allow the comments to retain context.
Function objects don't take very much space at all. The operating system and memory available are going to be what decides in the end how this memory is managed. This is not going to really impact anything on a scale which you should be worried about.
When loaded on my computer, a relatively blank jsfiddle consumed 5.4MB of memory. After creating 100,000 function objects it jumped to 7.5MB. This seems to be an insignificant amount of memory per function object (the implication being 21 bytes per function object: 7.5M-5.4M / 100k).

jsFiddle Demo