There are a bunch of papers do research on resizable garbled circuits. But I wonder why garbled circuits cannot be reused?

For example, the constructor constructs a garbled circuit of "AND" like this:

$E_{K_{u}^0}(E_{K_{v}^0}(K_{w}^0))$, $E_{K_{u}^0}(E_{K_{v}^1}(K_{w}^0))$, $E_{K_{u}^1}(E_{K_{v}^0}(K_{w}^0))$, $E_{K_{u}^1}(E_{K_{v}^1}(K_{w}^1))$

Then he sends this garbled circuit and $K_{v}^0$, $K_{v}^1$ to the evaluator.

Every time, he wants to evaluate the garbled circuit with an input $b\in\{0,1\}$, he just sends $K_{u}^b$ to the evaluator.

Other than letting the evaluator know that he may have the same input in different evaluations, I cannot think of other revealed information.