D1.1 and many other welding standards are concerned with the strength of a connection. A smaller weld than what is specified may not transmit the load from one member to another. The weld is smaller, so it is weaker.
If the weld is larger than that specified, it is unlikely to fail. It is bigger, it is stronger.
In the case of welder performance qualification, one is trying to assess the welder's ability to deposit a sound weld, i.e., free of unacceptable discontinuities. You are also attempting to determine if the welder can deposit a fillet weld of a certain size. 1/4-inch and 5/16-inch fillet welds are very common in the structural steel industry, if the welder can deposit a single pass 5/16-inch fillet weld during the test, there is a good probability he can do the same in production.
If the welder deposits a much large weld than the 5/16-inch specified,it is a case of the welder not following direction. In production, making welds that are considerably large than that specified is a waste of time, money, and consequentially, represents profits lost.
Best regards - Al