How to properly charge per unit of proof-reading?

Question

I've been doing a side gig proofreading a company's technical documentation for the past couple of months. The workflow is the company sends be a batch of technical articles for me to proofread and change, I do it in my own time and send them back the fixed copies of the files. They review my changes and there is often a bit of back and forth discussion about the changes. The company pays me X cents per word in the original article after I finish proofreading it. The issue I'm wondering about is that during the back and forth discussion, the company will sometimes add a couple of sentences to the article and ask me to verify whether the new sentences make sense. Since these sentences were not part of the original article I technically don't get paid for that work.

I have two questions about this situation:

1. How can I ask the company to pay me for those sentences without coming off as a penny pincher? Should I be getting paid per word of the completed article instead? What's a clean way of bringing up such a topic without annoying the employer?

2. A couple of days ago I read on this site that as a freelancer I should be asking to be paid in advance of doing any work. Given that they have been paying me for my work, is this something that I should bring up?

I've looked around the website but haven't been able to find something that matches my situation closely enough, so I decided to ask my own question.

Answer 1

The agreement is already in place - you get paid for the words in the original article. To change the agreement, you and the employer need to agree to the change.

If you want to set your foot down with these extra sentences, I would look to see if your contract dictates what happens to new lines added to the articles. If there is nothing about it, then I would let them know in your next back-and-forth that you can't proof read the new sentences, as they are not part of the original contract.

Will this piss them off? Likely. Are they taking advantage? Possibly.

You'll need to be firm, but polite. If they push back that the extra sentences are to be included, ask for them to be included in the payment, since you are putting in just as much work for this new content as the original.