Sam Allardyce's team have now taken just one point from a possible 12 at Upton Park, while Paul Lambert's men saw their run without finding the target extended to 375 minutes.
Villa striker Christian Benteke came closest to preventing a stalemate when he cannoned an effort off the crossbar after the break, but ultimately neither side could find the breakthrough.
West Ham responded immediately. Mark Noble's knock-back seemed destined to present Jack Collison with a glaring opportunity, only for Yacouba Sylla to make an impressive interception.
Against the run of play, Weimann got in behind the Villa defence after 17 minutes. Ravel Morrison, more obviously in the side for his attacking qualities, sprinted back to make a challenge, with referee Howard Webb waving away the young Austria international Weimann's firm appeals for a foul.
Wingers Jarvis and Downing continued to thrive for West Ham, and the latter's excellent cross on the half-hour mark set up Collison, who failed to get his header on target.
Villa captain Ron Vlaar made a fine sliding challenge to stop a Morrison throughball sending Jarvis clear just past the hour mark, and that proved to be the former Wolves player's last action, as Jarvis and Collison went off for Joe Cole and Carlton Cole, the latter handed his first home appearance since returning to Upton Park after being released at the end of last season.
First, Benteke's powerful header from Matthew Lowton's high cross from the right came back off the crossbar.
Then West Ham raced up the other end and Downing's clever reverse pass set up Nolan, who, from eight yards, dragged his shot wide.
