In Iron Man (1), after Tony escapes from the Ten Rings and goes back home, Obadiah gets Tony to keep a low profile. I don't understand why Obadiah would do it and why Tony would agree to his advice.
Keeping Tony away from others lets Obadiah manipulate the situation.
Offscreen, Obadiah calls for the board of Stark Industries to remove Tony, conveniently while Tony is not attending board meetings trying to keep this "low profile". Tony still trusts the man, so he presumes this is a good idea.
Obadiah informs him of this only after Tony stops trusting him. The reporter drops the photo that the Ten Rings has Stark weaponry, and Tony knows someone has to be double dealing, and confronts Obadiah, at which point he stops the act and makes his intentions clear. After that, there's no more chance for manipulation and Iron Man starts flying his missions.
Upon returning from captivity Tony announces Stark Industries will no longer produce weapons, and the stock price plummets.
Obadiah asks Tony to lay low, to prevent the price from dropping anymore (this is Obadiah's explanation to Tony.) Tony accepts this because he trusts Obadiah and because Obadiah runs the business side of Stark Industries.