A Fano variety over $\mathbb{C}$ with Gorenstein singularity is called weak Fano if the anti-canonical divisor is nef and big.

Are there finite families of weak Fano 4-folds with canonical Gorenstein singularities? Moreover, in what sense a set of Fano varieties is called "in the same family"?

Any comment on finiteness of Fano varieties are very welcome!