Will there be any difference in solution for a weighted and unweighted graph? I mean is there any relation between weight and solution?

I was working on max-cut problem. To do I have been given a graph of unweighted version, and I have to convert it into weighted version. I did it using qiskit. Now I was playing around the code, hence I have been assigning some arbitrary weight value to the edges. Then I found some confusing results. The more I am changing, the more I am unable to decode what is going on?

Lets elaborate, imagine this is my unweighted version graph (it is taken from qiskit textbook), in this graph weight is 1. so whenever I am changing the value of weight from 1 to 3,4,5 etc. I am not getting the desired solution {11011} or {00100}.