The northerners, who have won their last five matches, moved to 51 points from 23 games, leading second-placed Lyon by two points and Paris Saint-Germain by three after both their main rivals also claimed three points.
Lyon had Lucas Paqueta to thank in a 1-0 win at second-bottom Dijon while champions PSG eased to a 3-0 victory at bottom side Nimes courtesy of goals by Angel Di Maria, Pablo Sarabia and Kylian Mbappe.
Mauricio Pochettino's side were without the suspended Neymar but the Brazilian's absence was barely felt in a one-sided game at the Parc des Princes, three days after PSG slumped to a 3-2 defeat at Lorient.
That loss had handed Lille the lead in the standings and they kept it in authoritative fashion.
They went ahead nine minutes after the break when Turkey forward Yazici fired the ball under the bar from Jonathan Bamba's cross before Weah tapped in after being set up by substitute Luiz Araujo to double the tally.
David wrapped it up a minute from time after a fine one-two with Jonathan Ikone.