In the formulation of governing equations, which option does not signify the characteristics of a weight function?

In the formulation of governing equations, which option does not signify the characteristics of a weight function? Correct Answer Weight function must denote a non-dimensional quantity

In the development of the weak form, we consider a typical element and multiply its governing equations with weight functions. They can be interpreted physically for a given equation; for example, in the momentum equation, the weight function must be interpreted as velocity. For the representing volume change, weight function is like pressure. Thus, it can be a dimensional quantity.
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For a governing equation, what does one conclude from the weak formulation if it does not contain boundary integral involving weight function?