Earl tears are not an argument.
They may accurately represent an emotional state, and that might be persuasive, as you suggest. A gun can be persuasive too, but it's not an argument either. Unfortunately, when tears are offered in lieu of arguments it's more often than not a manipulation.
Manipulation with tears or a gun îndicate that probably this person doesn't have a sound argument to make. Perhaps, this is how they have gotten their way before without having to formulate an argument at all.
But in adult world we have to treat each other with the respect of a sound argument and not emotional threats.