All the information you need is here:
http://www.delta.com/traveling_check...cked/index.jsp
Short answer is that for the trip to and from the US, you get 2 x 23kg. For the intra-US flights you get 2 x 32kg.
The relevant sections are:
For travel within or between the United States and Canada, U.S. Virgin Islands or Puerto Rico and all travel to Brazil: SkyMiles Medallion® Silver, Gold, Platinum and Diamond members, Million Milers, SkyTeam Elite and Elite Plus members, and Alaska Air MVP & MVP Gold Members traveling in Economy may check up to two bags up to 70 lbs (32 kg) each at no charge on Delta and Delta Connection operated flights. The benefit applies to up to 9 people traveling in the eligible member's reservation.*
and
For all other travel regions: SkyMiles Diamond, Platinum, Gold and Silver Medallion® members, Million Milers, SkyTeam Elite and Elite Plus members, and Alaska Air MVP & MVP Gold Members traveling in First or Business class may check three bags up to 70 lbs (32 kg). In Economy class, SkyMiles Diamond, Platinum, Gold and Silver Medallion members, Million Milers, SkyTeam Elite and Elite Plus members, and Alaska Air MVP & MVP Gold Members traveling outside the US, Canada or Brazil will be allowed two or three bags up to 50 lbs (23 kg) depending on the standard cabin allowance. The benefit applies to up to 9 people traveling in the eligible member's reservation.*
As an FYI, you will get better traction on these sort of questions by asking in the relevant airline forums (in this case, Delta). The alliance forums are generally pretty quiet.