Balta returned to the sound of boos from Hawthorn fans in the Tigers' 16.13 (109) to 6.8 (44) loss at the MCG on Sunday, after spending a week on the sidelines because of his court-imposed curfewÂ
It was his first match since being sentenced last month for assaulting a man on December 30 last year.
Balta was also targeted during a win over Gold Coast - his only other appearance this season after serving a four-match suspension related to the assault - three days before he was sentenced.
"Every supporter group can do what they want, but what we can do is put our arms around him and support him," Yze said after Sunday's match.
"We've just got to make sure that doesn't tip over the edge and create any anxiety and pressure for him.
"We've got to support him as best we can throughout the week and he knows how much we love him.
"As I said, every supporter group can do what they want, but I would be hoping the Tiger Army don't do that to other players."
Balta, who is free to play against winless West Coast next Sunday, limped off in the final minutes against Hawthorn after appearing to roll his ankle.
"He copped a bit of a corky," Yze said.
"He was trying his best to get our ball movement going from our back half, but he's OK. He's a battering ram."
Yze also backed Tim Taranto despite the experienced midfielder gifting Hawthorn a goal by shoving James Sicily over and giving away a 50-metre penalty.
Sicily had thrown Maurice Rioli to the ground after catching the Tiger holding the ball, and Taranto rushed in to remonstrate.
Most players on the ground became involved in the ensuing melee.
"One hundred per cent, he's got to fly the flag," Yze said.
"Sicily's a fiery character and he got into one of our younger players, so for our vice-captain to step in and fly the flag ... there's obviously a method to it.
"But as a coach, when one of your players is going in to help one of your younger players and fly the flag and lead by example ... he might have overstepped it but I'd rather him do that than not go in there at all."