Here are some things to consider.
1) Why are you splitting up your outcome variable into coarsing groupings? You lose variance by doing so. That may be theoretically fine, or after some modeling you may see that it is appropriate to do so. But modeling 3 levels with either a linear model (probably not appropriate, but could be after model checks) or an ordinal/multinomial logit/probit will likely give you different results than modeling the outcome as continuous. I wouldn't jump to the conclusion of breaking down the data in that way before doing some testing unless my theory was really strong; I bring this up because you haven't provided any details on why you want to do this.
2) It is relatively simple to account for differences in states - just include them as covariates. Population, for example, can be included as a covariate (consider entering it in logarithms rather than raw). This will adjust your results by each state's population. However, if this is survey data and you have sampling weights, those weights may account for that, in which case including population as a covariate would have a different interpretation.
3) To model state differences you could enter them as fixed effects (K-1 dummy variables, where K is the number of states). Alternatively, you could consider a random coefficient model, where the state is a normally distributed random effect. There are tests for this that are important to use. Without knowing more about what you are modeling or what you have done, I won't get into the details too much here.
You need to provide more context to your statement "I can't tell which results are significant." What results? Did you model it? How? What are you looking at that is confusing?