The 38 year old Rangers defender has been capped 61 times for his country and featured in all 12 of the recent European Championship qualifiers, but has disappeared from the scene since Burley took over as national coach at the beginning of the year.
"That's my second game in charge and Stephen McManus and Gary Caldwell have formed a good international partnership as well as club. %uFFFD so other people have got to take it off them.
"They have shown they can do well at this standard. I have said that (Caldwell] has grown in stature. When he's been put under pressure and things have maybe went a little bit against him he's got stronger and that says a lot for the boy."
Against the Czech Republic, the Celtic duo performed as well as anyone and Burley believes the defence looked more vulnerable when McManus had to go off, replaced by Christian Dailly. "We made changes and that's when we conceded goals," he said.
However, his assistant manager, Terry Butcher said it would be wrong to rule Weir out completely.
"He's had a phenomenal season. I would never discount Davie. He has a strong desire to play for Scotland. I think George had a chat with him the last time and he has not ruled him out at all. Look, England brought back Beckham. In qualifiers you need as many people as you can, especially those who have experience to get you through.
"I wouldn't rule Davie Weir out of playing in the World Cup but it might be a bit of a tall order. He could still help his country get there, though, and I'm sure he'd want to feature and be a part of that."