First just as a warning I believe it's not possible to have PDF file with the lower size then word file, especially if we are talking about DOCX files.
Now regarding your requirements, you can check out the solutions mentioned
here (Some are free and some are paid, but be careful because sometimes with free solutions you get what you paid for...).
Also just a thought, from my experience images have the biggest impact on PDF file's size, so what you can try is just optimizing all the images in word files and then use any solution (free or paid) in order to convert them to PDF.