Brown got into two games with the Giants last season, but played more extensively with New Orleans the previous four years.
Weems lost last season to a shoulder injury.
Collins, who was signed as an undrafted free agent, could also see time at left guard. But the rookie is taking his first reps with the team at right tackle with
"We think he has the physical ability to play a couple of different spots," coach Jason Garrett said. "He was a tackle for most of his career in college but did play guard. We see him as a guy who can maybe do both of those things as he goes.
"The big thing for him is to try to get him acclimated as quickly as we can. So right now he's going to play right tackle for us. He and Darrion Weems are competing at that spot in Doug Free's absence and we'll just see how that unfolds."
Leary has started 31 games for the Cowboys over the last two seasons. Weems did not appear in a game during the 2014 season after being placed on injured reserve due to a shoulder injury.
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