What’s next in the Alex Jones trial: The jury will hear more testimony and weigh additional damages.

After ordering the conspiracy theorist Alex Jones to pay more than $4 million in compensatory damages to the parents of a child killed in the mass shooting at Sandy Hook Elementary School, jurors will return on Friday to consider awarding punitive damages.

The jury, which announced the partial award on Thursday after several dramatic days in court, is scheduled to hear additional testimony about Mr. Jones and his misinformation-peddling media outlet Infowars that is likely to include discussion of his net worth and his company’s.

Compensatory damages are based on proven harm, loss or injury, and are often calculated based on the fair market value of damaged property, lost wages and expenses, according to Cornell Law School. Punitive damages are designed to punish especially harmful behavior and tend to be granted at the court’s discretion, and are sometimes many multiples of a compensatory award.

Mr. Jones is accused of defaming the families of children killed in the mass shooting at the Sandy Hook school in 2012, falsely describing them as actors participating in a hoax (he acknowledged this week that the shooting was “100 percent real”). The award announced on Thursday for Scarlett Lewis and Neil Heslin, whose 6-year-old son, Jesse Lewis, died in the attack, was the first to arise from several lawsuits filed by victims’ parents in 2018.

A trial for damages in another of the suits was scheduled to begin next month in Connecticut, but it could be delayed because of a bankruptcy filing last week by Free Speech Systems, Infowars’ parent company. Lawyers for the families criticized the move as another attempt by Mr. Jones to shield his wealth and evade judgment.

Starting on Friday, lawyers for Ms. Lewis and Mr. Heslin are expected to delve more deeply into Mr. Jones’ financial situation, calling an economist as an expert witness. This week, they presented records showing that, at one point in 2018, Infowars made more than $800,000 a day.

The parents had sought $150 million in compensatory damages.