I'm a non-native author and I have a revised paper that has been edited for good English before the first review. Now I made major changes, but still a large part of my essay remained as before. What is the best way to get my revised paper edited for English and flow without having to get charged for the whole (relatively long) paper again? Was someone in a similar situation?
I am a native English speaker, this is based off my experiences proofreading papers for others in my lab who are not native speakers.
Changing even a small section of a paper can have repercussions throughout the rest of the paper in unexpected ways. Also, as important as it is that the English in the changed sections is correct it is also important that those changed sections flow appropriately with the rest of the paper.
To help with both of these issues it is best to have the entire paper proofread again. Even as a native-English speaker, I have others proofread my paper after revisions because of the above issues. It can be helpful to somehow mark the changed sections and request that the proofreader be aware that those areas were changed.
ESL here and this is how I usually deal with similar situations.
Go back to the same editor for a reduced rate
It will not hurt to ask. Highlight the parts that you changed, and send over with an inquiry if he/she is willing to look at it again, with heavier grammatical checks in the highlighted sections and then overall flow, at a reduced rate.
Form a weekly writing group
This is a pretty stressful method but it's one of the best decisions I have made. Form a writing group with 2-3 colleagues. We model after this article. All my partners are native speakers, and I often get English-related advices and even edits from them.
You may feel inadequate (I did at the beginning), but don't. Being an ESL has its appeal. If I can understand their work, it's very likely that native audience will also understand their work. In a way, I am their coal mine canary.
I agree with Nahkki that changing parts of the paper influences the remaining paper as well. The reason is that when reading / reviewing a paper you can easily spot different writing styles (especially if you have parts coming from native and non-native speakers). Having different styles within a single paper distorts reading and makes a bad impression. In your case, I would suggest to let proof read the whole paper again.
However, in general, I suggest to write papers with co-authors who are either native speakers or know how to write. Only this way, you can actually learn how to write, which is an important skill often underrated. I cannot see how you can learn writing scientific articles without having the opportunity to talk and discuss why some sentences or paragraphs are written in "native" way. So, my advise is to get people working with you and learn from them.