The controversial award on thirty eight minutes when Eddie Forrest was harshly adjudged to have handled as he slid in to clear from James McAlistair.
Forrest was furious at the decision and Ayr felt that justice was done when Weatherson skied the ball yards over the top.
Ayr soaked up Morton's pressure and always looked threatening on the counter attack with Jerome Vareille shaking off a series of challenges before rifling the ball over.
Ayr keeper Mark McGeown did well to cut out a McAlistair cross but United almost won it at the end when sub Gareth Wardlaw raced into the box before being foiled by a great save by David McGurn.
Morton boss Jim McInally said, "Our front players need to be braver and we seem to lack a bit of self-belief but hopefully going top of the league will give us that".
Ayr boss Robert Connor said, "Morton are the best team in the league so we are pleased to come away with something".