The leak took place in 2012 but was only revealed last month by the bank.
Details leaked included client names, BSB numbers, account numbers and NAB identification numbers.
The breach affected migrant banking customers: those who recently came to the country and opened accounts.
Weissenberg owns the domain names nab.com and nab.net, and the former hosts a dating website. The bank's domain is nab.com.au.
A report in The Australian said that Weissenberg owned several other domains such as supersleazy.com, sexyneighbours.com and teaseclub.com.
The AFR said he also owned sexpornhost.com, porncocktail.com, liveteendreams.com, welovenakedgirls.com and adultorientatedmaterial.com.
In a media release, Peter Coad, NAB executive general manager for international branches, said: "As we have said previously, we have been, and continue to, take action to ensure this group of migrant banking customers’ accounts are secure.
"Although this has been a complex process involving multiple international jurisdictions, all parties — including the email account owner — are taking this extremely seriously and NAB is working hard to resolve this matter for our migrant banking customers as soon as possible.
"From our productive and helpful discussions with the email account owner, we understand that the email address to which the correspondence was incorrectly sent, is not actively used and our customers’ emails have not been wrongfully used. We are confident that there has been no unusual activity associated with these migrant banking accounts and we continue to monitor 24/7.
"We take full responsibility and have apologised to our migrant banking customers and assure them that we are working hard to improve and strengthen our processes to make sure this doesn’t happen again."
iTWire has sought comment from Weissenberg.