The official novelisation gives some insight into Obi-Wan's thought process. In short, at the start of Episode II he's far too distracted by the bigger picture to concentrate on what he views as an adolescent crush and he certainly doesn't think that Padmé has any romantic interest in Anakin:
The eagerness with which the Padawan had embraced his new duty set off
warning bells in Obi-Wan’s head, but he had allowed the mission to go
forth anyway, mostly because he knew that he’d be too busy following
the leads he hoped he could garner here, uncovering the source of
By the time he's noticed what's going on, he raises the issue with Mace Windu and gets slapped down. He considers pushing the matter further but comes to the conclusion that Anakin's lack of emotional detachment is a form of test that he'll simply have to overcome. Note that he doesn't even consider the alternative:
“But he still has much to learn. His skills have made him… well-”
Obi-Wan paused, trying to walk that delicate line. “-arrogant. I
realize now what you and Master Yoda knew from the beginning. The boy
was too old to start the training, and…”
“He has a… an emotional connection with her. It’s been there since he
was a boy. Now he’s confused, and distracted.” As he spoke, Obi-Wan
started toward his star fighter. He climbed up the cockpit ladder and
into his seat.
“So you have already stated,” Mace reminded. “And your concerns were
weighed properly, and did not change the decision of the Council.
Obi-Wan, you must have faith that Anakin will take the right path.” It
made sense, of course. If Anakin was to become a great leader, a
creature of prophecy, then surely his character tests must be passed.
Anakin was waging one of those tests right now, Obi-Wan knew, off in
seclusion on a distant planet with a woman whom he loved too deeply.
He had to be strong enough to pass that test; Obi-Wan just hoped that
Anakin recognized the trial for what it was.