Khawaja scored back-to-back centuries at the Sydney Cricket Ground in a stunning return after more than two years out of the Test side.
Konstas, 20, misses out after a poor tour with the bat in the West Indies, while Weatherald has been included after topping the Sheffield Shield runs list
The hosts lost six wickets in the first session for 94 runs after resuming on four for no loss on Day 2 of the fourth Ashes Test in Melbourne.
Australia's opening partnership has been the subject of much debate since David Warner retired and remains unresolved less than a month before the World Test Championship final against South Africa.
Usman Khawaja celebrated his recall to the Test arena after two years in the wilderness with a stylish 137 to drive Australia to a declaration on 416 for eight shortly before the close of play on the second day of the fourth Ashes Test on Thursday.
Labuschagne underlined the cricket adage that "catches win matches", while England counted the cost of dropped chances in Adelaide.
Usman Khawaja said the black armband he wore in the first Test against Pakistan was for a "personal bereavement".
'I think he's got the technique, he's got the patience to partner up with Uzzy (Khawaja) to allow himself to score big.'
Former No. 1-ranked Test batter Marnus Labuschagne will be pushed up in the order to open alongside Usman Khawaja.
Khawaja suffers injury scare in warm-up game against Sri Lanka
Usman Khawaja hit an unbeaten century to give Australia the upper hand on Day 1 of the fourth and final Test against India in Ahmedabad on Thursday.
Khawaja to battle Head for openers' spot as Australia name squad for first two Tests.
Australian middle-order batsman, Usman Khawaja received an Ashes berth, and, opener Phillip Hughes was also lucky to retain his spot in the squad, after a poor performance in India.
Australia head coach Andrew McDonald hinted at a rejig in the top order after misfiring in the World Test Championship final defence against South Africa at Lord's.
The brother of Australian cricketer Usman Khawaja has been taken into custody by counter-terrorism police
The visitors, who are 2-0 behind in the four-Test series for the Border-Gavaskar Trophy, finished the frenetic opening day 47 runs ahead with six wickets in hand.
Australia cricketer Usman Khawaja on Saturday appealed to people from every sphere of life to tackle the COVID-19 pandemic with all the seriousness. He was among the many cricketers to have expressed their concerns over the current crisis.
Statistically, Head's series stands apart. Among all players to score more than 600 runs in a single Ashes, he is the only one to do so at a strike rate north of 75 -- a reflection of how decisively he altered the tempo of games.
Travis Head smashed a blistering century at the top of the order to set up an eight-wicket win in the Ashes series opener in Perth.
In-form batsman Usman Khawaja should be part of Australia's World Cup plans despite the imminent returns of Steve Smith and David Warner, former captain Ricky Ponting has said.
India's biggest challenge could come from an unexpected source -- Pakistan's mystery spinner Usman Tariq.
Usman Khawaja's fairytale comeback has presented Australia with a selection headache, and captain Pat Cummins conceded it would be hard to drop the in-form batsman from the fifth and final Ashes test against England in Hobart next week.
'The tailenders should have looked to bat with Jamie Smith. Really poor from the batters towards the end. The plan should have been to give him the strike and let him do the heavy lifting.'
Former Indian cricketer Ravichandran Ashwin hailed New Zealand batter Daryl Mitchell as a "brainy cricketer" who is capable of making the best out of his limits as a player and someone who can give a franchise 400-500 runs batting at number three or four during a tournament.
Uncapped New South Wales batsman Usman Khawaja was named on Tuesday in Australia's 14-man squad on Tuesday for next month's two-Testseries against Pakistan in Britain.
Travis Head said he was loving life as a Test opener after recording his third century of the Ashes series to help put Australia in a strong position after day three of the fifth Test on Tuesday.
Khawaja said he was still good with bat in his hand and that "age is just a number".
England's Joe Root conquered his final frontier with a first Ashes century in Australia as the tourists pushed past 300 on day one of the second Test in Brisbane on Thursday despite a six-wicket haul from pace spearhead Mitchell Starc.
Australia will have to dust off the cobwebs but are still fancied to successfully defend their World Test Championship crown against equally ring-rusty South Africa in the final at Lord's.
Cameron Green and Alex Carey guided Australia to an emphatic five-wicket victory against England, to claim the series 4-1, on Day 5 of the fifth Ashes Test on Thursday.
Australia's Travis Head says he is prepared to open the batting once more against England during the ongoing Ashes series after his second innings display in the first Test in Perth last week led the home side to an eight-wicket victory over the tourists.
Australia's two-time World Cup winning captain Ricky Ponting says senior batsman Usman Khawaja was axed from the national team due to his inconsistency but he is not willing to write him off yet. The 33-year-old Khawaja was recently left out of the Australia's annual list of contracted players after he was dropped midway through last year's Ashes.
The 31-year-old was out of action since undergoing a surgery on a torn meniscus which he had sustained during their Test series against Pakistan in October in the UAE.
'It's a double-edged sword, but I'm enjoying it.'
Australia captain Steve Smith has declined to rule out a surprise return for fast bowler Pat Cummins for the second Ashes Test against England.
'They're those little moments as a squad that I think have got us across the line to four wins this series.'
Steve Smith and Travis Head hit centuries to help Australia dominate the third day's play by stretching their lead against England in the fifth and final Ashes Test.
Taking his 17th Test five-wicket haul, he finished with 7 for 58 off 12.5 overs.
'(I was) getting too deep into my technique and trying to be too perfect instead of just playing with what I've got...'
