I would read carefully this paper

[link Point to another website Only the registered members can access]
This paper gives you a lot of hints how to do it. Also look up the references !!!
Again, listen to the Whitsen lectures as he talks about this and the regression process.

Yes, the weights needs to be used and the parameters used NEED TO BE constrained so as not to go out of the realistic range for the parameters. Again, this is in the paper and in the Whitson lecture.

Now this is a bonus, Prof. Whitson SHARES his lectures which he gives in Norway University

[link Point to another website Only the registered members can access]
This is education for FREE. I rarely see this done this well, even in places where you would think this should be the norm.

I will try to contact someone who may, I repeat may, help. No guarantee.

You are dealing with a near critical fluid which is not the norm for me and some of my friends. The one things I do know about Near Critical fluids is that it is very very easy to THINK you have matched the data when in fact you have not gotten it right at all.

When I have something I will share it here.