The bond between Sonny and Tom probably made him jealous.
What makes you believe this? I see no sign of jealousy in Michael, at least not in terms of brotherhood.
Mike wanted to be closer to Sonny, but Tom was always there. It made him resent them both.
I think that neither the film nor the novel show us that Michael was jealous.
"When Hagen had entered the room Sonny had come rushing to embrace him. Michael realized with a faint twinge of jealousy that in many ways Sonny and Tom Hagen were closer than he himself could ever be to his own brother." - The Godfather, page 96.
Forgive me for bringing back such an old topic, but I've been reading the novel again (it seems like the 100th time) and I got the itch to return to this forum and discuss some of the finer details.