Help Reduce Document Overhead

When you're save as the document with Illustrator be sure to not tick the "Retain Illustrator's editing features"*  option, which will prevent having two files (AI + PDF) in one, and thus reduce its weight.

*Translated from French, I do not know the exact item in English

I am unsure if this will be helpful but I have just done three tests to accertain which process is the best for reducing the size of pdf documents with fillable fields. I converted a MS Word document to pdf using three options. 

1. Saving the document as an Adobe pdf
2. Opeing the document in Adobe Acrobat Pro
3. Printing the document to Microsoft print to pdf

All three had exactly the same pdf document size, however when I added a field to number 3 the document size doubled. 

Number 3 did not prepare the form efficiently which led to me having to insert a number of missing fields.

The document overhead storage was significantly less in numbers 1 and 2.

Hola. One trick that I have used when I have recieved large, layered PDF files is printing the file to a PS file and distilling the PS file.  The settings on the distiller can be set to an acceptable, low resolution setting.  When printing the PS file I also use "outlines" for the fonts and subset the fonts.  This reduces the possility of editing the PDF afterward but creates a considerably small file.  Let me know if that works for you.

How did you save the file from AI? 

Also, what is your OS (and what release)?

Which version of Acrobat (and what release)?

Typically Document Overhead is embedded fonts. Do you have a number of unique fonts embedded in the document?

A trick that often works is simply saving the file under a new name in Acrobat. It forces an optimization and can reduce the file-size dramatically.