If the methods described in the other messages do not lead to the desired result, you'd have to do a bit more analysis to find out what causes the big file size.
In order to do that do Save as other… --> Optimized PDF
In the dialog appearing click on Audit Space Usage and try to interpret the results (or show them in in a new answer to this question).
If the share of fonts is very high, it means that this form has been in the works for some time, and it is very likely that different fonts were tried, or you indeed use several fonts in the fields.
What happens when you select a font for a form field, is that it immediately gets fully embedded. That is necessary; it can not be subsetted, because we don't know which characters will be used when filling the form. If you are using a "modern" font with several hundred glyphs, it easily adds several hundred kB to the file.
When you change the font for a field, the newly selected font gets fully embedded, and so on. The problem is that, even when you do a Save as… which should clean up the file, Acrobat does not throw out the no longer used fonts.
Good practice for preparing a form for distributing is to again take a blank form document, clean it up as good as possible, so that its file size gets minimal, and then you copy the fields from your last development version to this clean blank document, and do a Save as… Note that this is not the common procedure where you simply replace the pages…
This procedure does give you the minimum file size.
Hope this can help.
Max Wyss.