I will assume that it is a fillable pdf file. The only way for you to get more words in there is to have Acrobat, the full version, and use it to modify the word limit in each field. OR to print it out and use the hold fashion typewriter.
Whoever made the fields for you to fill in later has limited the number of characters in that field.
I think "jots" will help you out with Acrobat. DO KEEP IN MIND THAT IT IS ILLEGAL TO PIRATE SOFTWARE. Pursue this possible avenue at your own personal risk.
You might try asking your university/library/professor if it/they have Acrobat on a computer that you might use for a few hours to fill out secondaries. All the professors that I am in contact with tend to use Acrobat for their grant proposals, writing papers, etc. It is rather universal for document delivery these days.