They may have won the FA Trophy for the last two years but, make no mistake, Grays went into this tie as clear underdogs.
Missing six players through injury or suspension, including influential captain Stuart Thurgood who was named on the bench after failing a late fitness test, was hardly a promising backdrop for manager Andy King.
But King took a tactical gamble, adopting a 4-5-1 formation with former Everton star Danny Cadamarteri on his own up front and regular right-back Andy Sambrook in the centre of midfield.
And the ex-Everton midfielder felt vindicated as goals by Cadamarteri and John Martin gave Blues an impressive win against a side who have turned the Wessex Stadium into a fortress.
King said: "Sometimes you do things and you look like Bill Shankly, other times you do it and you look like an idiot. I think it worked.
"I want to be known as a League manager but the Trophy means something to the club and the fans, possibly creating history by winning it three times on the trot."
Match-winner Martin admitted he could understand Leicester City's interest in Cadamarteri and revealed his team-mates were doing everything possible to keep the striker at Grays.
He said: "Danny is a great player and his work-rate is unbelievable. He's done us a real good favour coming here.
"It will be nice if he stays a bit longer and we're all trying to get in his earhole, but I don't know what's going to happen.
"We were struggling for numbers with a lot of injuries. We played a formation which may have looked a bit defensive but I think worked very well.
"It was hard work and we were under pressure for the last 25 minutes, but we showed a lot of character to come through it."
Weymouth captain Ben Smith glanced a header just past the far post from Abdou El Kholti's early corner and El Kholti, a thorn in Blues' side during the recent league match, was just wide after showing good skill in the area.
But the Terras relied far too much on long balls in the first half and Cadamarteri stunned the home crowd with a classy opening goal after 21 minutes.
The 27-year-old, who recently returned to action after failing a drugs test while with Bradford City, played a sharp one-two with Martin before finding the top corner with a clinical finish from 15 yards.
Weymouth appealed in vain for a penalty when Richard Logan appeared to be fouled and the same player miscued wide seconds later as Raphael Nade's knockdown created a clear chance.
Justin Richards, who played on the right side, went close to doubling Grays' lead seconds after the interval with a strong shot which curled agonisingly wide of the far post.
Weymouth levelled in controversial fashion on 50 minutes, Logan converting confidently from the spot after Jamie Stuart was penalised and booked for fouling Nade.
Blues went ahead again on the hour when Cadamarteri played Martin through, Jason Matthews did well to parry but the former Leyton Orient midfielder comfortably converted the rebound.
Ashley Bayes produced three fine saves to thwart Smith as the Terras at last stepped up the pace, but Weymouth boss Garry Hill admitted his side only really came to life in the last half-hour.
Hill said: "The first goal by Cadamarteri was a great goal. He's played in the Premiership and he showed some great quality.
"We should have gone on to win from 1-1 but we got done on the counter-attack for their second goal against the run of play.
"From then on, it was 25 minutes completely in their half, but we didn't take our chances and we got punished.
"I don't think we should take anything away from Grays because they came here and worked hard.
"You can see why they've won the Trophy for the last two years and they don't want to lose their hold on it."
Blues' league form suggests another play-off push may be beyond them this season, but don't rule out a record-breaking third successive triumph in the competition they've made their own.
By Matthew James
Thanks to the Thurrock Gazette for the report.