OK, here's the scoop, from Julian, his brother runs the Thunderbolt: http://AmbergrisCaye.com/thunderbolt/
The Thunderbolt leaves San Pedro town at 7am on Sundays. It leaves
Belize City at 9am too. Only on Sundays.
The Thunderbolt is the ideal boat to take on Sundays since it departs at 9am sharp from Belize city.
There are other passenger boat services from the city but I am not sure
what their regularly scheduled runs are!
>RE: limit of 40 lbs. of luggage.
This does sound odd. Maybe there is a mistake somewhere.