Functions with small support have small circuits
Consider the AND function:
$$
x_1 \land \cdots \land x_n.
$$
Its support size is $1$, and its circuit complexity is $O(n)$. By negating inputs, you can get a circuit for any function whose support size is $1$. By ORing together $k$ such functions, you can get a circuit of size $O(kn)$ for any function whose support size is $k$.