There are a few ways in which an argument can be weak.
It could be weak on its own merits (e.g. the facts are not substantial, or the logic is not entirely sound). In this case, the words tenuous, insubstantial, shaky, flimsy and others suggested here may be variously appropriate.
However, in business situations the central issue is often the relative importance of an argument, rather than the correctness of the argument.
- For example, the secretary's argument may be reasonable on its own ground, but there may be far more important or compelling arguments against his point of view.
- This is a common situation in audits, because there are usually correct arguments on both sides of an issue, so it's not so much a question of whether the arguments are incorrect, but rather whether one argument is more important than another (e.g. risk of fraud or default is more important than risk of missing an earnings estimate).
In such situations where you want to point out that one argument is weaker than, less important than, or secondary to another, you can use the term marginal:
The secretary's argument is marginal.
The secretary's argument is marginal compared to case we are making to write off this business expense in the audit.