No boats and no rental car really does limit you a lot.
Besides Bonaire you could also try Curacao, sometimes the flights are a little easier or cheaper than Bonaire. Try Kura Hulanda Lodge, Habitat, or Sunset Waters. They are all a distance away from town. If you go to any of these places without a car you will mostly stay there, a taxi would be very expensive. They all have shuttles but the normal schedules are not usually convienient, though sometimes you can make special arrangements for cheaper than a taxi would be out there. Habitat and Sunset have good dive shops and shore diving on site. I wouldn't personally choose them for a honeymoon though as the accomodations are rather basic. Kura Hulanda is beautiful and would make a great place for a honeymoon if you want to get away from it all and not leave the resort. I would not suggest it for boat diving as they are very unreliable on running a boat. But if you are sticking to shore diving the house reef there is great, by far the best of them on Curacao. KH doesn't have the easy convienience of 24 tank and locker availability like the other places so you have to plan ahead for any diving outside shop hours.
There is also an op on Curacao called the "Dive Bus" which would enable you to get to other shore diving sites without a car. They are closer to town and would not pick up at the places I already mentioned, so you would need to stay someplace in town or nearby. They are based in the area near Breezes, Lions Dive and the Seaquarium resort (timeshare condos.) You could stay at one of those places and have shore diving on site though IMO not as good as the more remote places. But taking a taxi downtown to shop or eat easily done here. You could also stay at the Marriott which is very nice and is supposed to have a decent shore dive, I think the dive bus would pick up from there, not sure. Or you could stay at the Kura Hulanda Lodge right downtown (sister hotel of Lodge) which would be a really nice honeymoon place, lots of stuff you can walk to, I assume the dive bus would pick up - just no shore diving from there.
You can also get packages split between the KH lodge and hotel and, that might be good in your situation. Shore dive some days at the KH Lodge, then explore the city from the KH Hotel and use the dive bus.
It's a rare place in the Carribean that will have other than 80cf alum tanks. (Though some will also have 63s.) Soft weights are also very rare. Is there a reason you need soft weights, you can use hard weights in pretty much any BC and there are belts you can get with pockets that can take hard weights that are more comfortable than webbing, if comfort is the issue.