A tiny p-value does not mean a bigger edge

Two signals are tested. Signal A returns $p = 0.001$; signal B returns $p = 0.03$. A colleague concludes, "A's edge is much bigger and much stronger than B's, since its p-value is 30 times smaller."

Explain why a smaller p-value does not imply a larger effect, and give a concrete counterexample where B actually has the bigger edge despite the larger p-value.