The guilty plea comes after settlements that Wal-Mart reached with California and Missouri in 2010 and 2012 on the same charges.
He did not resign after settlements for any of the prior wrongdoing that took place under his purview for which the firm paid about $10bn in fines.
Motley Rice, known for its tobacco, lead paint and asbestos litigation, initially represented 53 cases, and still has 30 after settlements.
Microsoft struck agreements with customers in North Carolina, Tennessee, North Dakota, South Dakota, Kansas and the District of Columbia, after settlements in four other states earlier in the year.
The report is being issued as international health groups like the World Health Organization are trying to keep attention focused on smoking after settlements in lawsuits under which major cigarette makers agreed to restrict advertising and finance anti-smoking campaigns.
Mr. Weiss, Milberg Weiss and the other defendants were charged with a scheme using plaintiffs that had been paid to help the law firm to file class-action suits ahead of competitors, which brought the partners higher legal fees after settlements.
