Just after finishing my OW certification, I did a dive out of Little River, SC to an old steamer wreck lying in 50 feet of water. I had not yet started buying my own equipment so rented from the dive operator. I had been debating on whether to buy weight belt or integrated. I had trained using a belt but felt like the integrated made more sense. Anyway, as is usually the case, the gear from the dive operator was very used and of couse had a weight belt. Most of the onea they had were too short to fit me and the only one they had on board that was long enough was way long. On the 2nd dive, I was at the bottom fanning the sand looking for relics when I suddenly felt the belt sliding off my waist. Somehow, the buckle had come unclinched and was leaving me. I was able to grab the end of it just as it came off and I was ganging there upside down in the water with my now underweighted body wanting to go to the surface. I was finally able to get the belt back around my waist but due to its extra long length I could not get the end if it back into the buckle. And to top it off, my instabuddy had somehow gotten separated from me and there was no one with me to help.
I ended up having to surface while holding the belt arounf my waist with both hands. I did a very slow ascent and fortunately didn't suffer any ill effects from the adventure.
You can probably assume from this that when I did buy my BCD, it was weight integrated.