I think that weak-left is a little strange, just think a little of the operators used by mathematicians that always follow a hierarchy. 

A parser is mostly done using grammars : see http://docs.python.org/3.1/reference/grammar.html.

Defining *-product to have stronger priority than the @-product, and this last having stronger priority than +, will make the changes in the grammar easier.

I'm now convinced of the usefulness of @ and @@ too but I also think that you must think of other uses than only for numpy. In other words, numpy is a the good argument for this new operators, but this can also open new perspectives for other uses.