The early church seems to do it weekly, Acts 20:
More evidence for weekly Lord's supper can be found here.
Meeting together was linked with the Lord's supper in 1 Corinthians 11:7 On the first day of the week we came together to break bread. Paul spoke to the people and, because he intended to leave the next day, kept on talking until midnight.
Outside of the Bible in Didache:20 When you come together, it is not the Lord’s supper that you eat. 21For in eating, each one goes ahead with his own meal. One goes hungry, another gets drunk. 22What! Do you not have houses to eat and drink in? Or do you despise the church of God and humiliate those who have nothing? What shall I say to you? Shall I commend you in this? No, I will not.
23 For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread, 24 and when he had given thanks, he broke it, and said, “This is my body, which is for you. Do this in remembrance of me.” 25 In the same way also he took the cup, after supper, saying, “This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me.” 26 For as often as you eat this bread and drink the cup, you proclaim the Lord’s death until he comes.
Little Trinity Church does it every Sunday.But every Lord's day gather yourselves together, and break bread, and give thanksgiving after having confessed your transgressions
More evidence for weekly Lord's supper can be found here.