Weston, who arrived at the Banks's Stadium in the summer of 2007, told the Express and Star: "We've had a decent run and it's as good a chance since I've been at the club. If we keep as many players as we can fit there's no reason why we can't mount a serious challenge.
"We've got to be realistic, it's going to be difficult but the manager and (assistant) Martin (O'Connor) have instilled belief into the squad that we are good players.
"There's more confidence but I wouldn't confuse it with complacency because we've won some games without playing well. We've said for weeks we're not far from being a good team."
He continued: "I don't think we're under pressure. We're not being touted as promotion favourites like Leeds, Charlton and Norwich. If anything we can go and enjoy it and give a good account of ourselves."