As you saw through very thick stock, each saw tooth shaves out an enormous amount of waste. In order to maintain a reasonably productive feed rate, there has to be somewhere for that waste to be stashed out of the way until the teeth emerge from the cut. Otherwise the gullets between the teeth fill up and stall further advance until they've cleared the stock. Blades with about 3 teeth per inch (tpi) have large gullets which can accommodate as much waste as you'll generate by sawing through thick stock, and they'll handle anything less substantial with no trouble at all.

In principle, the wider the blade, the higher its beam strength and the better it can maintain straightness. Wider, however, isn't necessarily better. Almost all US woodcutting bandsaw blades over 1/2" wide are .035" thick