What factors does the specific rotation value depend on?

I remember looking up the specific rotations of various protonation states of one or two amino acids and coming to the conclusion that protonation state affected the specific rotation.  It occurs to me to wonder whether or not this might be a conformational effect, but I do not know.

Sure! And thank you!

So specific rotation = (observed rotation)/(concentration x path length)

Based on this, it would appear that specific rotation does in fact depend on concentration as it's part of the equation.

Did I get this right?

For molecular weight, I'm asking, does specific rotation value have any dependency on molecular weight? So a higher molecular weight, with all factors otherwise the same, has a higher specific rotation value?

I don't think it depends on molecular weight. Not sure about concentration though.

Observed rotation = (specific rotation) x concentration x path length.

The observed rotation depends linearly on concentration, but concentration does not change the specific rotation.  The same is true of path length.

When people tabulate specific rotations, they include the temperature at which the experiment was performed.  What does this imply?  I am not aware of any trends regarding molecular weight.

Specific rotation depends on the chirality of the molecule. Changes in chirality result in changes in specific rotation. An old way of measuring the success of a diastereoselective reaction was measurement of specific rotation. It is one of the pre-NMR techniques used to characterize reactions.

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So specific rotation = (observed rotation)/(concentration x path length)

Based on this, it would appear that specific rotation does in fact depend on concentration as it's part of the equation.

No, doesn't follow. When you change the concentration observed rotation changes as well and the [itex]\frac{observed~~rotation}{concentration}[/itex] ratio remains constant.

At least that's for ideal solutions, for real ones, especially highly concentrated, things can get a bit more complicated.

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For molecular weight, I'm asking, does specific rotation value have any dependency on molecular weight? So a higher molecular weight, with all factors otherwise the same, has a higher specific rotation value?

Specific rotation is a property of a compound. You can't increase molecular weight of a compound without changing into it into another compound, with its own specific rotation.

You could ask whether - in general - compounds with higher molecular mass have higher specific rotation. The answer is: no.

Would you please provide your thoughts first?  Then we can help you.  I will give you a small hint to get started.  Regarding your question about concentration, it is critical to distinguish between observed rotation versus specific rotation.  If you write out the equation for observed rotation, this might become clearer.  Regarding molecular weight, I am not sure that I understand your question.  Any one compound only has a single molecular weight.