The ex-Manchester City stopper, a former England Under-21 international, said competition for the number one spot was a fact of footballing life and hopes to be involved against Chelsea this evening.
Weaver said: "It's just how it is. I've had it all through my career when you see a goalkeeper walking through the dressing room one morning and you think, 'What's he doing here?' but there's only one reason why he's here.
"If it wasn't me it would be someone else, but there won't be a problem with me and Brian.
"To get a chance to be back involved at this level is something that I perhaps thought might not come."
Burnley boss Brian Laws has also backed Weaver to stake a claim.
Laws said: "Goalkeepers are at their peak between the age of 30 and 36. I spoke to people in Scotland including the Scotland manager and they couldn't speak anything but good about how he performed.
"This is a real opportunity for him to get back where he belongs."
Weaver and fellow new signing Leon Cort, the central defender who has joined from Stoke, will both be in Burnley's squad to face Chelsea this evening. Andre Bikey is also included after returning from the African Nations Cup.
Graham Alexander is struggling with a calf strain but Chris McCann is hopeful of shaking off a knock on his knee.
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