delete large amounts of blank space (not a blank page) on a fillable form

If he/she created the form, then he/she should have the application that he/she used to create the form. 

While one Acrobat can do minor edits in a document (fix a spelling, change a date), massive changes to the layout are just not possible. It is ALWAYS better to go back to the original document and make any changes you're talking about. 

About the only option you have is to export the PDF into a Word document, make the changes, and convert it back to a PDF from Word. 

Unfortunately, you'll have to recreate and/or reset the form fields at that point. Depending on the nature of the fields, that will be fairly easy to not so easy. There's no way for me to guess on that.