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In vertex algebra theory, fusion rules are described as the dimension of thevector space of intertwining operators between three irreducible modules. Wedescribe fusion rules in the category of weight modules for the Weyl vertexalgebra. This way we confirm the conjecture on fusion rules based on theVerlinde algebra. We explicitly construct intertwining operators appearing inthe formula for fusion rules. We present a result which relates irreducibleweight modules for the Weyl vertex algebra to the irreducible modules for theaffine Lie superalgebra $\widehat{gl(1 \vert 1)}$.

On fusion rules and intertwining operators for the Weyl vertex algebra