Weaver was left in limbo with Pearce's successor yet to be confirmed and, rather than having to prove himself to the new boss, the 28-year-old chose to secure his future by signing a three-year deal with the Addicks.
"One minute we were talking about a testimonial and the next we weren't talking at all and I found that disheartening," Weaver told the Manchester Evening News.
"I was told that the contract offered while Stuart Pearce was manager was no longer on the table and that I would have to basically go on trial for the new manager. I found that a bit of an insult, given that I played more than 30 games last season in the Premiership and cups."
Weaver made 205 appearances for City and will be best remembered for his penalty saves in the 1999 play-off final victory against Gilligham at Wembley.
He then suffered a string of injury problems, making just two appearances for City between March 2002 and August 2006, but started last season as first-choice, making 31 appearances.
However, Swedish international Andreas Isaksson took over in goal towards the end of the season and established himself as the new first-choice.
"My agent Paul Stretford made it clear that I didn't want to leave City, where I had spent most of my adult life, but in the end it became clear that it was time to move on," added Weaver.
"I will probably never again experience the special bond I have with City's fans and, for their sake, I hope the season is a great success. They deserve to see a winning team.
"Now I have got to get on with my new life. Alan Pardew made me feel extremely welcome and did in 15 minutes what City couldn't in 6 months.
"Former Blues Paddy McCarthy and Ben Thatcher are here, so I will not be a stranger in the dressing room."
Goalkeeping coach Eric Steele added on the City website: "He's a true professional, and the way he battled back from an injury that would have finished many people speaks volumes for him.
"Even when he wasn't in the first team towards the end of last season his dedication in training never let up, and I hope everything goes well for him."