Jarrett Bousquet of Titan Sports Management says he believes the incident is "being swept under the carpet" because it occurred just before the Christmas break and Weber wasn't immediately diagnosed with a concussion.
"I was very surprised and disappointed that Fistric was not suspended for his hit on Weber," Bousquet said Wednesday. "The NHL is raising awareness about concussions and trying to eliminate these types of hits so I don't think that it's too late to right the wrong in this situation.
"I think the NHL should re-visit this hit if they do in fact want to raise awareness and eliminate hits to the head, as well as send a message to repeat offenders."
Fistric hit Weber with a forearm or elbow to the head in a meeting between the Stars and Predators on Dec. 23. Weber finished the game and took Monday's morning skate before being made a scratch against Detroit. The Predators announced Tuesday that he was suffering from a concussion and would be out indefinitely.
The NHL didn't have clear video of the play and elected not to levy any supplemental discipline against Fistric, who would have been considered a repeat offender after receiving a three-game suspension earlier this month for a hit on Islanders forward Nino Niederreiter.
Weber rode a stationary bike on Wednesday without any setbacks but sat out his second straight game later that night against Minnesota. He's considered doubtful for Friday's game in St. Louis as well.
"Even if he feels good, it's the next hit that's worrisome if he is not 100 per cent," said Bousquet. "I think as a precaution it would be better if he took Friday off and then (went) from there."
Weber was a finalist for the Norris Trophy last season and entered play Wednesday with the third highest point total among defencemen. The 2010 Olympian has eight goals and 29 points in 35 games.