Police officer Beau Lamarre-Condon also outlined a self-defence claim, and prosecutors revealed the discovery of alleged crucial evidence in recent months, on the blockbuster trial's second day.
Lamarre-Condon, 31, has pleaded not guilty to murdering Mr Baird and his new partner Luke Davies and stealing Mr Baird's belongings six months earlier.
He admits entering his one-time partner's home in February 2024, disguised and armed with his police pistol, but he insists he did not plan to kill the occupants.
Mr Baird's mother Helen and sister Kourtnee gave at times tearful evidence in the NSW Supreme Court trial on Tuesday.
The 26-year-old relayed concerns about Lamarre-Condon's growing obsessions after they dated briefly in the summer of 2022 and 2023.
"Jesse would be at the gym ... he would receive messages (from Lamarre-Condon) saying 'you looked really good in the gym tonight'," Kourtnee Baird said.
"He was fearful, he was scared."
In contrast, Mr Baird's mother only met Mr Davies once but could tell how taken her son and his new partner were, the jury heard.
"It was early days but they were both smitten with each other ... they were great together," Helen Baird testified.
Mr Baird, who also worked as an AFL goal umpire, sent his mother of a photo of him and Mr Davies at a Pink concert, saying "Luke's my boyfriend".
"I sent a big love heart and said 'I'm so happy for both of you'," she said through tears.
Less than two weeks later, Lamarre-Condon entered Mr Baird's Paddington house armed with his police pistol and heavily disguised with a motorcycle helmet.
The killer's barrister on Tuesday told jurors the senior constable was there to collect belongings and didn't want to be recognised.
He armed himself as he was not allowed to leave it unattended in his car, as per police protocol, John Stratton SC said.
The defence would argue a struggle ensued after Lamarre-Condon was surprised by the presence of Mr Baird in the kitchen.
The police officer's gun then went off twice, killing the 26-year-old, the jury was told.
Mr Baird did not recognise the accused because of his disguise, Mr Stratton said.
After the struggle, the gun flew across the room, the officer's barrister said.
A call to triple zero was made from the house where operators heard someone say "Get out, f*** off" followed by a shot, the jury was told on Monday.
While the Crown alleges the call was made by Mr Davies moments before he was shot, Lamarre-Condon's lawyer said his client made it.
Mr Davies emerged from the bedroom holding a knife, picked up the discarded gun and a second deadly struggle occurred, the defence would argue.
"He never planned to kill or ever cause any harm to anyone ..." Mr Stratton said of the defendant.
"His case was it was in self-defence."
Lamarre-Condon's barrister conceded his client had done some "stupid things" when the brief relationship between he and Mr Baird ended in April 2023.
Mr Baird treated it more casually than the police officer, jurors have heard.
The officer does not dispute he looked through his ex's phone and deleted contacts and text messages.
Lamarre-Condon also allegedly abused his position as a police officer to obtain CCTV from a pub to see who Mr Baird was meeting.
But Mr Stratton disputes the senior constable exhibited threatening behaviours before the fatal incident in the Paddington house
Prosecutor Brett Hatfield SC used the last hour of his opening address on Tuesday to claim crucial evidence inside the house was discovered on the eve of trial.
A bullet hole in the bedroom door was found concealed with putty, fresh paint and a stick-on hook when officers re-examined the scene in July, Mr Hatfield said.
"The firearm was discharged close to the door with Luke Davies on the other side of it," the prosecutor said.
The NSW Supreme Court trial continues.
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