Galadriel's intentions.

[Boromir88]

That's very possible Dol Guldur. Gandalf says in The White Rider "She told me he (Boromir) was in peril." Perhaps Galadriel caught hints of the Fellowship beginning to fall apart. She tested each member to see who would stick with Frodo, and started the "breaking of the Fellowship." Not for evil purposes, but possibly to realize the sooner the better? Perhaps she just awoke in Boromir the "sleeping giant" because maybe the longer it went "dormant" the worse it would be?

Edit: The fellowship was also hit with constant bad luck, and it almost seemed destined to break apart. I mean first the wolf attack, then the storms on Caradhras, then all the evil in Moria, then the problems down Anduin and the argument between Aragorn and Boromir. It just seemed constant doom hung around the Fellowship and Galadriel realized it was best to break it.

For Aragorn, it's not that he might have not been loyal to Frodo (I mean if he wanted to he could have easily taken the ring in Bree and going to Rivendell), but just that his path was ment to be different. Not to go along with Frodo, but to save Minas Tirith. As Aragorn makes an oath to Boromir....

"No!" said Aragorn, taking his hand and kissing his brow. "You have conquered. Few have gained such victory. Be at peace! Minas Tirith shall not fall."~emphasis mine

With that oath, I think it becomes clear that he wasn't ment to stick with Frodo, and follow him to the end, but to try and save Gondor.