The 22-year-old had a year to run on his current deal but has now signed a deal to keep him at Priestfield until the summer of 2012.
Weston arrived from Leeds last summer and played a major role in the club's promotion and follows fellow star men Simon King and Andy Barcham in penning new deals this summer.
Manager Mark Stimson said: "It's great news. We've recently signed Simon King on a long-term contract and now we've signed Curtis up for three years.
"I think the kid's got great potential and I think he realises that now. I look forward to seeing him play in League One and hopefully he will have an effect like he did in League Two.
"It's a very, very good signing for the club."