According to sources, the team branded Smith with a stringent and potentially costly "weight clause," which will require Smith to stay at or below 350 pounds during the season.
Smith, who is listed at 335 pounds, will risk losing a significant portion of his salary if he is caught above the 350-pound limit.
Smith's weight could be monitored each week by the Bengals during the season, one source said.
A second source added that it was one of several major sticking points in the negotiations, which resulted in a 30-day contract dispute, and Smith missed all of training camp and three preseason games.
One of the knocks on Smith entering the draft was that he's had trouble maintaining his weight in the past. The Bengals were so concerned about it that they sent representatives to visit Smith for a surprise weight check just a few days before selecting him with the No. 6 overall pick this past April.
Smith, whose deal includes $21 million guaranteed, and maxes out at six years and $42 million, is trying to claim the starting right tackle job in Cincinnati. Bengals coach Marvin Lewis has said throughout training camp that Smith would get the chance to compete for the starting job once he got into camp.
The Bengals' offensive line was one of their top priorities in the offseason. The offense finished last in the league in 2008 in large part because of the line's ineffectiveness.
Smith has practiced with the team this week, but it is unknown if he will play in Thursday's preseason finale against the Indianapolis Colts.
James Walker covers the AFC North for ESPN.com. Information from The Associated Press was used in this report.