Because the rim is the critical ingredient for the strength of the wheel, it's best to use the spoke size for which the rim was designed. For bicycle rims, that's almost always 14ga. A few of them are drilled with larger holes, but those are the same extrusions that were manufactured with 14ga spokes in mind. It's always possible to use spoke washers to accommodate hubs that have been drilled with too-large holes
You can increase the effective capacity of a given rim by using thinner spokes, but you decrease its capacity by using thicker spokes. A tightly laced wheel seems rigid and unmoving, but to carry weight, it must be able to flex in proportion to the applied weight. Thin spokes can maintain tension and resist unscrewing as this happens; thick spokes can't.