opine
To state your opinion in a thoughtful, somewhat formal way.
To opine means to express your opinion, especially in a somewhat formal or thoughtful way. When a teacher opines that students learn better through hands-on projects, she's sharing her professional judgment. When a food critic opines about a restaurant's new menu, he's offering his considered view.
The word carries a slightly formal tone. You probably wouldn't say your friend opined about lunch options, you'd just say she gave her opinion. But a senator might opine on proposed legislation, or a chess coach might opine about a player's strategy.
It often suggests someone is stating a view based on experience or expertise. When a scientist opines that a theory needs more testing, she's drawing on years of knowledge. When a grandfather opines about the best way to build a treehouse, he's sharing wisdom earned through experience.
The word doesn't mean the person is necessarily right, just that they're offering their viewpoint in a thoughtful, considered way. Everyone's entitled to opine, but some opinions carry more weight than others depending on the person's knowledge and experience with the subject.