Resubmission of arxiv paper after rejection
I am not particularly "new to the game", and I still often submit preprints prior to acceptance. To me, this is the entire point of an arxiv or PeerJ preprint - after acceptance, I can usually just self-archive the camera-ready version and don't even need a preprint server to ensure priority.


  will the preprint of the current version that is already on arxiv affect the acceptance of the newer version (asssuming that the journal has no policy against arxiv preprints) ? If yes, what can I do to prevent that?


Why would it? The fact that you have an earlier version of the paper online at a source that, according to your assumption, does not count as prior publication should not matter at all. You are allowed (some would say required) to improve on your work between unsuccessful submissions.

Also, the existence of your preprint probably does not say much more than that an earlier version exists, not whether and where it has been submitted, or how often. It would take a particularly unreasonable reviewer to hold it against you that your paper may have been rejected somewhere in the past.

The only time when the existence of the preprint may be awkward is you made a significant mistake in your previous version and need to change some relevant study outcomes because of that. I would not worry about minor updates to the results, especially if you collected new data in the meantime, but if the core results and message of the paper somehow dramatically changes between versions a reviewer who is aware of this may question the validity of your science. For instance, I have once reviewed a paper that was strongly arguing that A leads to B in the preprint, but in the version I reviewed they suddenly flipped and said that A clear does not lead to B, but instead to C - without any new data. As a reviewer, this does raise a lot of red flags.