Sorry, I got the weddings mixup. What was Littlefinger’s motive for the Purple Wedding? Doing it to assist the Tyrells or to get Sansa seems too weak a reason.

Ah, I gotcha. Well, there’s a number of things Littlefinger gains from the PW:

1. Gives him an in with the Tyrells.
2. Punishes Tyrion for tricking him, divides the Lannister faction against itself, and ensures that Tyrion won’t be there to provide assistance to the Lannister faction down the road.
3. Ensures that Tyrion can’t accuse him of the murder of Jon Arryn or the attempted murder of Bran Stark or the framing of Tyrion Lannister. 
4. Frees Sansa, which gives him potential claims to Winterfell and maybe Harrenhal and  Riverrun. 
5. Ends Sansa’s marriage, which he wants for both political and personal reasons.
6. Focuses Tywin’s attentions on the trial and not, for example, on the Vale.
7. Delays the production of a Baratheon/Tyrell heir. 
8. Punishes Cersei for denying him Sansa. 
9. And most importantly…giving him a wonderful warm fuzzy feeling inside because he’s the smartest man in the world.