“Then I'll file one every day.”
As a verb, file means to formally submit a document or complaint. File a complaint makes an official complaint, and one refers back to a written complaint. Other combinations include file a report and file a claim for insurance.
“your voice would carry more weight.”
Carry weight means to have influence or importance. Carry more weight means that a person's views will be taken more seriously.
“Sign me up. Turns out I have a lot to say.”
Sign me up. enthusiastically asks to join, from the idea of adding your name to a registration form. Turns out … shortens It turns out that …, introducing something realized or discovered. Tina discovers that she has plenty to say.