The primary benefits, as listed above, are a diplomatic boost with the faction and the potential for grandchildren down the line.
When married your male children will always stay with you and have the other faction's daughter join you, while your female children will always go to the other faction. Horribly sexist, I know.
When grandchildren grow up they have a chance to join either of their parent's starting faction. It seems weighted towards their joining their mother's faction, that is, your son's kids will probably defect away from you while your daughter's kids will probably defect back to you. It isn't set in stone, just seems like it happens that way most often.
Because children inherit the abilities of their same-sex parent you can end up getting the abilities of other Sovereign's this way. So for example I marry my daughter to Kul-Kulan's (or whatever his name is) son, they have a boy, that boy grows up and joins me, now I have a grandchild with the Organized trait.
The formulas that determine children starting stats are still a little screwy, for example even if both parent's have 2 base move I frequently get kids with 1 base move, which sucks. Also no matter how pumped my two parents stats are (STR, DEX, etc.) the children and especially grandchildren tend to "even out" to 10 (because the AI tends to not level their kids much so all their stats stay at 10). The only exception is Essence which has been stated to always be "50-100% of the higher parent's essence."
One thing I do before sending my daughter's off to marriage is level them up a bit and equip them with a basic set of armor. It only take 3-4 easy battles to get them to level 3, put the level ups in hit points or dexterity, and buy them whatever armor you can afford. This increases their survivability considerably even when controlled by the AI.