The Sulphurites make the long trip down to Devon aiming to end the Grecians' seven-match unbeaten run in League Two, but knowing they will have to improve on their two most recent performances in order to do so.
They were beaten 3-1 at home by Crawley last week then threw away a two-goal lead as they drew 3-3 with Rochdale on Saturday afternoon, with individual errors proving costly on both occasions.
And Weaver, who insists there "is not a lot wrong" Town's performance levels on the whole, believes that some of the mistakes his players have been making stem from them failing to handle stressful moments in games as well as they might.
“Sometimes it’s about managing the stress in the game and that excitement level. It’s a different set of emotions and this level is less forgiving," he said ahead of Tuesday nights clash at St James' Park.
"It’s handling the stress management during a game. If you take the 10 seconds before each of the goals we conceded on Saturday, there was a bit of stress in certain situations where people have dived in or made the wrong decision and that can be improved now as it’s ongoing and we’re learning harsh lessons. One mistake cannot always lead to us giving away a goal.
“Individual moments cost us, but we have a style of play that you could see and if we cut out the individual errors then the style of play could have produced a really convincing win at Rochdale. We scored three goals and created a lot more. We looked like scoring every time we went forwards.
"There’s not a long wrong, so we’ve got to stay true to ourselves. This is still a step up which we are getting used to. Of course there are aspects to improve upon, but we’ve got to say patient with a very loyal bunch of players, not chop and change, change the style, change personnel."
Town travel to Exeter 13th in the League Two standings, while the Grecians currently sit fourth having won their last three matches on the spin.
Weaver's men are unbeaten in their previous three meetings with City, drawing two and winning once.
Their victory over Matt Taylor's side came in last season's corresponding fixture, with strikes from Brendan Kiernan and Jack Muldoon securing a 2-1 success.
The sides played out a 1-1 draw when they faced-off in North Yorkshire earlier this term, Josh Key's late leveller cancelling out Muldoon's first-half penalty.
Kick-off at St James' Park on Tuesday evening is at 7.45pm.