Villa dominated the first half with neat finishes from Agbonlahor and Weimann sandwiched by shots against the woodwork from Fabian Delph and Ashley Westwood.
The opener arrived shortly before the quarter-hour mark when Weimann's deft touch gave Agbonlahor just enough room to turn and shoot low past Hull goalkeeper Allan McGregor from 10 yards (meters).
Villa doubled its lead in the 36th when newcomer Michael Dawson's loose ball was won by Delph, spread wide to Kieran Richardson and finished in two touches by Weimann.
Hull hit back when Nikica Jelavic's 72nd-minute header was turned home by Villa full-back Aly Cissokho with a huge deflection.
Delph brought the home fans back to their feet with a fine run and shot before Jake Livermore took aim at the other end. His 25-yard strike was headed for the top corner but Villa 'keeper Brad Guzan made his first save of the match a crucial one.
Both sides had chances in stoppage time, Darren Bent dragging wide from a good position for Villa and Sone Aluko firing directly at Guzan with the visitors' final chance.
After three matches, Villa has seven points and Hull four.