If I wield two melee weapons with defensive 2, how many black dice does this add to the opposed attack roll? 2 or 4? The book is very gray on the subject.

Page 207 of Edge says multiple sources of defense do not stack. However, if one melee weapon had defensive 3 and the other had defensive 2, you'd get the highest defense available. In that case, it would be 3.

Thanks I appreciate it.

The subject of “Two Weapon Combat” has been discussed extensively on this forum.

You are likely to have much more luck finding those posts if you use that term when using the search interface at the very top of the page, instead of a term that might be appropriate in another game.