co-authorship for software adaption Beside the determination of a property of newly prepared compounds, I aimed for a comparision with the value of the same property for already literature-known materials.  During this meta-analysis I became aware of a program that may assist this process.

In a first attempt, the software performed better than I expected.  It looked like the potential field of application was more general than the one initially described in an accompanying publication for this program. I contacted the developer to check if the results still were reasonable with this "version A" of the softwared.  The developer was surprised the algorithm implemented performs so well even in cases initially not envisaged / estimated as "too difficult" back then the software was released initially, confirmed the results, provided hints "how to do even better" and improved the software further into "version A+".

The question is in the context of writing up for a publication.  The intended paper's barycentre will not be the aforementioned meta-analysis with this software.  Certainly the developer will appear in the literature references for the initial publication presenting the software.  Where however discern between a special acknowledgement in the publication, on one hand, and co-authorship, on the other?  As "version A" was performing well, offering already the insight sought-after, yet "version A+" does so even better?

So far, to express gratitude for the assistance provided by the developer in the section "acknowledgements"  is the minimum to do.
As you're feeling, this is a greyish area.  To me, it depends on the paper itself.  If the paper really focuses on using this software to do something, this would nudge me toward offering authorship -- and I would ask the developer to fully participate in manuscript prep.  The credibility/knowlege of the developer may well make your paper better, and might be of help depending on how it is received by the referees.

If the use of the software amounts to a sentence in the methods section, I would acknowledge.