I have never been to Belize, so I perhaps I may say things that I don't understand but anyway...
Why the dive planning to 130' ? Is there something exceptional (e.g. stalactites?) that cannot be seen at 100'? I'm asking, because from my experience, divers tend to have their saying when the instructor/DM gives the briefing for the dive, and they discover it's going to be a rather deep one. Why divers care? Some do try to respect their certification limits, others know that such a deep dive means also a *shorter* dive, and/or it may limit the following dives for the following day/s, or they may be concerned of insurance issues if something goes wrong and it was discovered that they deliberately planned a dive beyond cert level...
So, unless something extra spectacular is waiting at 130', most divers will prefer to spend longer dive and compromise max depth to 100' instead of 130'. Again, this is my experience from our part of the world (for me, the one and only Blue Hole is at the Red Sea
and usually there's not much difference between 130' and 100' - unless one goes MUCH deeper to ~200').
Anyway, what I understand from OP it is all about a simple, rather common phenomenon: what divers usually call "Air Hog on board".
What surprises me in this thread, is the flaming being targeted at the instructors/operators, with suggestions ranging from to confiscate his certification up to "let's feed him to the sharks"- rather on the divers themselves...
What I mean, is that I usually meet divers complaining that the instructor/DM cut off the dive after "only 15 minutes" because of a "bloody $@#!! AirHog" and why everyone has to suffer short dives ("we pay a lot of our best earned $$$ to come here"), typically followed by after dive discussion (that is, comparison of how much air each one got out of the dive, with suspicious unbelieving frowns upon the AirHog, who lowers his face with shame), and comments of "why such a short dive!!"), then suggestions as what to do with the AirHog (revoke his certification, fish him to the sharks next dive, toss him overboard immediately).
I'm of course exaggerating a little bit- I've never met an airhog that was actually thrown from boat- but I've got a feeling that the OP was also slightly exaggerated too, in order to make a point.
What would you do when discovering one among your group is an AirHog (who also paid his best $$$ to come diving)?? Would you complain the instructor/DM is having him share some air (and *prolong* your dive), or "damn, he was the best instructor I've ever met- he cut the dive after 10 minutes because we had an AirHog situation on board"??? Common, be honest, tell the truth...
And what if the AirHog was YOU, or your son? Would you notify beforehand the instructor and the group, asking for some consideration (or larger cylinder), or be shy/afraid of letting it known, for the fear of being ridiculed (at best) or fed to the sharks/thrown overboard (at worst)?? I WAS an AirHog, when at same age and experience of poor little Tim. Now I guess I'm okay, nobody will complain about me being the cause for shorter dives- on the opposite (they now start whining why they always have to wait too much for me to end the dive), but it did come with experience, as I suspect you all know.
Tim? If he would ask here on SB "Guys, I've got only six dives after cert, airhog- should I book a trip to BGH??", I'd probably recommend him not to waste his money- to acquire some more experience and then book his trip to GBH (or wherever), as he will enjoy much more the dives instead of focusing on his buoyancy skills and air consumption. But he made his choice, and the instructor actually tried his best to have the rest of the group unaffected by the hog's presence in the dive?
But hey, all these guys in the group were actually certified divers? Why did they agree to such a dive? As far as I know, 130' is beyond certification from AOW, or it's different over there in the western hemisphere? No self responsibility? Nobody asking why such depth, what happens from insurance point of view if something goes wrong? etc etc. That's why I'd imagined from reading OP that most flaming comments were going to be towards the divers and not the instructor/operation.
On the good note for operators, I understand they do placed an extra air tank with regulator- such a practice is not very common over here, and considered an extra precaution. I mean, for regular boats/liveaboards (i.e. sport divers). Tech cruises will have oxygen (or 50% O2) bottles on trapeze...