The backup quarterback spot is up for grabs.
Brock Osweiler, who signed a free agent deal with the Texans on March 10, is the starter.
Behind him, Tom Savage and DeAndre Hopkins will compete for the understudy's role.
Head coach Bill O'Brien said the competition's "going well" after OTAs, minicamp and the first practice of training camp.
"I thought both of those guys practiced well today," O'Brien said. "We split the team up into two groups for certain drills that we do so that we are able to get a bunch of guys reps, obviously including them, Tom and Brandon."
Savage is the most tenured of the trio in this offense, as he's in year number three with O'Brien and the Texans.
Weeden, meanwhile, was successful in a pair of 2015 contests for the Texans. He came off the bench in place of an injured T.J. Yates to guide Houston to it's first-ever victory in Indianapolis. A week later in Nashville, he started and led the Texans to a win over the Titans.
O'Brien liked what he saw Sunday morning, but wasn't ready to say who would be the backup.
"I thought that they executed well," O'Brien said. "There's no timetable on those types of things as far as who's number two, who's three, all those things. We are just into the first day right now. Those guys just need to keep trying to get better every day."
Weeden completed 26-of-32 pass attempts for 305 yards and three touchdowns. He didn't throw an interception, and also ran for a score in the win at Tennessee.
Savage was on the injured reserve in 2015 after suffering a shoulder injury in the preseason finale last August against the Cowboys.
The second day of training camp is Monday at the Houston Methodist Training Center.
The Houston Texans roster in photos. (Updated 9/7/2020)