The Sulphurites make the long trip down to Devon aiming to end the Grecians' seven-match unbeaten run, but knowing they will have to improve on their two most recent performances in order to do so.
Having conceded three times against both Crawley and Rochdale and ended up with just one point to show for their efforts, Town undoubtedly need to tighten up at the back if they are to have any chance of getting a result against a City side who have won three on the spin.
With Rory McArdle, Lewis Richards and Ryan Fallowfield all currently sidelined through injury, Weaver's defensive options are somewhat limited, though he still has centre-half Will Smith and the versatile Nathan Sheron waiting in the wings.
“We have conceded six goals in two matches, so of course that opens the door up for change," the Town boss told the Harrogate Advertiser.
“We will look at it [selection] because the last couple of performances do bring the likes of Will, and others, into contention. But that’s across all areas of the pitch.
“Everybody comes into consideration. They’re all my players aren’t they, I’ve signed every single one of them and there will be no favouritism. Decisions are made based on what I see in training and players’ attitudes.
“We’ve been making individual mistakes at the back, but, as I said to the lads after the Rochdale game, we defend as a team.
“We want to keep clean-sheets, however it’s not one single person’s fault that we’ve conceded six in the last two.”
Weaver has not forgotten that his side managed back-to-back clean-sheets prior to their recent disappointments against Crawley and Rochdale and says that he will not take any decision to alter things lightly.
He added: “I always want to come across as logical, not stubborn, but at the same time these decisions are made by Paul [Thirlwell] and myself alone and based purely on what the two of us believe is best for the team.
“I’m a deep thinker when it comes to this job. I analyse all areas because I want to give us the best chance to keep improving. I am so hungry for that.
“It can’t be forgotten that it was only two games ago that we kept back-to-back clean-sheets against two good sides.
“We’ve obviously not been able to repeat that in our previous two matches but the back-line in the Rochdale and Crawley games was the same one that stopped Bradford from scoring and not too different to the one we played against Mansfield.
“Of course we are looking to be better, but it’s not as simple as just looking at the defence and pointing fingers. If you analyse some of the goals we’ve conceded of late, the recovery runs haven’t been there. Our midfielders haven’t always been tracking their men or in a position to provide cover.
“It cannot always be the case that one mistake ends up costing us a goal.”
Town will kick-off their fixture at Exeter 13th in the League Two standings, while the in-form Grecians currently sit fourth having taken nine points from the last nine on offer.
Kick-off at St James' Park on Tuesday evening is at 7.45pm.