Weakly implicative selector sets of dimension 3

For an $n$-place Boolean function $\beta$, we define a class $K(\beta)$ of weakly $\beta$-implicatively selective sets, which are subsets of the set of natural numbers. The dimension of the class $K(\beta)$ is the number of essential variables of the function $\beta$. We describe, up to inclusion, all classes $K(\beta)$ of dimension 2 and 3, excepting one case.