Authorities are continuing to build a case against Chris Watts, the Colorado dad accused of killing his pregnant wife, Shan'ann Watts, and their daughters
Credit: Shanann Watts /Facebook

Authorities are continuing to build a case against Chris Watts, the Colorado father accused of killing his 15-weeks-pregnant wife, Shan’ann Watts, and their two young daughters — and a source close to the investigation tells PEOPLE that it’s a lengthy process.

The source says one of the most daunting tasks is unraveling Chris’ many suspected lies, including the allegation that he had an ongoing affair with a co-worker at the time of the triple slayings in mid-August.

“Every day, we learn more and more about him,” the source says in this week’s issue.

Under police questioning last month, Chris, 33, allegedly admitted he strangled his spouse of nearly six years, 34-year-old Shan’ann — but he gave a startling reason for doing so.

According to an arrest affidavit obtained by PEOPLE, Chris allegedly said that after he told Shan’ann he wanted to separate when she got back from a work trip, he saw her strangling their 3-year-old, Celeste, while their 4-year-old, Bella, lay “blue” and apparently lifeless on her bed.

In response, Chris allegedly claimed, he “went into a rage” and strangled Shan’ann.

But authorities aren’t buying his shocking explanation. Late on Aug. 15, two days after Shan’ann and the girls were reported missing and hours before the announcement that their bodies had been found on the property of Chris’ former employer, he was arrested.

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Credit: Celeste Sloman

While Chris has maintained a publicly stoic demeanor, a second source who recently spoke with him told PEOPLE that Chris has realized the gravity of the situation.

“It’s all beginning to sink in,” the source contended. “He’s in the mourning process.”

At an emotional funeral service for Shan’ann and her kids on Saturday, her family mourned their passing and celebrated their lives.

“Shan’ann was a woman of love,” Father John Forbes said. “She loved God, her family and her friends. She was a woman of determination. She had dreams to be fulfilled, and she worked towards to those dreams. She wanted to make a difference. She wanted to be an exceptional wife and mother.”

Forbes called Bella and Celeste “light for all those around them.” He also read a statement from Shan’ann’s father, Frank Rzucek.

The Watts family

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“I have so much to say, but I will make it short,” Rzucek said. “Daddy loves you. You are a wonderful daughter and a great mother. You are nothing but pure love, always caring for everyone. You will always be daddy’s little girl. Until we meet again, I love you with all my heart.”

Chris is being held without bond in the Weld County Jail. He is charged with three counts of first-degree murder and multiple additional charges, including unlawful termination of a pregnancy in the first-degree. He has not yet entered a plea.

His attorney is barred from discussing the case, according to a statement from the state’s public defender’s office, which represents him.

Meanwhile, authorities keep working to piece together the truth of what was really going on in the Watts family.

“There’s still a long way to go. He [Chris] had a lot of secrets,” says the investigative source. “But I know we will get to the bottom of it. You can write that down. It’s going to happen.”