Different size yields!?

I am currently working on a large blanket in which I took a 16 bit picture and am making a ton of granny squares and then sewing them together to make the picture.
I went and bought a whole bunch of yarn in all the colors I wanted, and some of the colors are different finishes. For example, one of the colors is a shiny blue, Red Heart Soft, while others are just flat colors.

After working on a few colors, I noticed that some of the granny squares I've made are different sizes although I am using the same tension, hook size and ply. I already researched blocking, and to an extent, that will work in making them uniform, but the thinner yarns, like the soft ones, will end up being thinner with blocking, which will make those sections of the blanket thinner and more holey than the rest. Which I really want to avoid.

What I want to know, is if there is a way to work the thinner yarn so that it will be similar in thickness to the regular yarn. For example, a finished granny square of red heart soft yarn is smaller and thinner than a finished square of red heart super saver yarn.

This is the pattern I am using for my squares
I am using "In The Round".