Former world 100 record holder Asafa Powell and Olympic relay silver medallist Sherone Simpson tested positive for the stimulant oxilofrine at June's national championships and were left out of the Jamaican team for the worlds in Moscow.
World 200 metres champion Veronica Campbell-Brown also missed out as she is provisionally suspended after failing a test for using a banned diuretic in May.
"There's no pressure," the quietly spoken Weir told reporters at the training track near Luzhniki Stadium where the world championships start on Saturday.
"We like to look on the positive side of life, we don't let any negative news get the best of us. We try to stay on a clear path and keep a steady head.
"We work with a young team and we are coping," Weir, wearing a black, yellow and green Jamaican team top, said leaning over the fence to talk to journalists after finishing his training session.
The 23-year-old, a training partner of six-times Olympic champion Usain Bolt, pointed out that Jamaica had plenty of up and coming athletes to replace the big-name absentees.
"We're just glad we have a young team that's coming up and we'll have a fresh team going into the championships.
"Our high school championship is doing tremendously good so that means that the young at least will be moving up in the long term," he said.
Weir burst on to the international scene at last year's London Olympics where he completed a podium sweep for Jamaica in the 200 behind Bolt and Yohan Blake.
Bolt is hot favourite to retain the world 200 title next week but asked if he thought he could beat his taller, faster, more famous team mate, Weir said: "Hopefully - it's stepping stones.
"I've improved on the turn and strength-wise - I'm much stronger than before and I'm running a more compact race, added Weir, who set a personal best of 19.79 this year when winning the Jamaican title in the absence of world record holder Bolt.
He returned to the Olympic stadium last month to win the London Diamond League in 19.89, his last race before the world championships.
Unsurprisingly, all the media attention in Moscow is on the sport's biggest showman Bolt, leaving Weir, who started his athletics career as a hurdler, to ply his trade unnoticed, something he said helped him.
"People don't expect a lot, people expect Bolt this Bolt that. That can help me a lot because I can go out there... and focus on running my race to my expectation and just focus on myself and nobody else."
(Editing by Justin Palmer)
