Weightman's night was cut short following the incident, with the 21-year-old needing to hold his right arm in a sling on the interchange - sitting out the rest of the match.
Duo Laitham Vandermeer (hamstring) and Tim O'Brien (calf) also had their evenings end early with injuries of their own in the third quarter.
The extent of setbacks further hinder Luke Beveridge's difficult start to the season, with the Whitten Oval club currently sat with a 3-5 record from the opening eight rounds.
Speaking after the game, Beveridge alluded to the short turnaround between games as a potential factor in some of his side's ailments on Friday night.
"It was a disappointing night for us and a night of carnage for us too when you lose three players in the fashion we did," the Dogs senior coach said.
"The five-day break might have got us a little bit with some of that unfortunately.
"It was high-end running the week before against Essendon and one or two of the guys in Tim O'Brien and Laitham, who are quite prone, went down, so that destabilised us a little bit."
The trio of injuries adds to an extensive casualty ward in Melbourne's west, with Tim English (hamstring), Josh Bruce (knee), Lachie Hunter (personal), Alex Keath (hamstring), Mitch Wallis (foot), Jason Johannisen (calf) and Mitch Hannan (concussion) among those unavailable.
Skipper Marcus Bontempelli was also out of action for Round 8 as the club decided to manage their four-time best and fairest winner, with Beveridge likely to recall his captain - as well as English and Keath - for next week's clash with Collingwood.
"We think he'll be ok," Beveridge said of Bontempelli.
"He's just had a series of things hampering him over a period of time that just came to a head this week.
"The week off will do him the world of good, and hopefully he'll be healthy come Friday night, but we'll see how we go next week.
"Maybe Tim English and Alex Keath might be available.
"Clubs and teams go through it. We're getting our lot at the moment unfortunately. We've just got to ride it out and persevere."
Port Adelaide were also forced to deal with injury concerns of their own, with defender Riley Bonner being assisted off the field after rolling his ankle in a marking contest.
Bonner was subbed out of the match and is anticipated to miss at least the next week, with senior coach Ken Hinkley suggesting the incident will be a "one-week, two-week" injury.
The win places Port Adelaide a step closer to the top eight, having claimed three consecutive wins to get their season back on track.
Hinkley's prospects will be buoyed by the likely return of veteran forward Charlie Dixon, who is set to make his playing return through the SANFL this weekend.
The Power will look to continue their winning ways next Saturday when they travel to Tasmania to play North Melbourne at Blundstone Arena.