There had been fears that the fly-half would be out of action until the New Year but Weir revealed he is targeting Edinburgh's back-to-back European games against Stade Francais in December for his comeback.
"I saw the surgeon and he was happy with the progress so far, with just over a week gone," said Weir. "I am chomping at the bit to be back as soon as I can.
"I will definitely miss rounds one and two [of the European Challenge Cup] but there is a nice double header against Stade Francais to welcome me back - into this competition anyway."
In his absence, Edinburgh suffered a 28-15 defeat to reigning champions Connacht last weekend - the fourth of the campaign to leave them tenth in the Guinness PRO12 table.
And acting head coach Duncan Hodge admitted they had worked on tightening things up ahead of hosting Benetton Treviso on Friday.
"We've been making too many errors and there are a couple of things in defence, so consistency is the key," he said.
"It's a great set of players and we've tried to change the training schedule and what we do in training this week, so it's small changes that will hopefully have an effect."
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