I used to use those cheap ones but had a near miss just like you describe - had a freshly assembled 289 Ford and was rolling it across the garage floor and the small plastic front caster hit a bolt on the floor and the stand started tipping over. I managed to prevent it but had to call out to a neighbor for help, because I was stuck holding the thing from completely falling to the floor, and I was losing my grip. The neighbor luckily saw right away what was going on and grabbed the other end of the block and helped me set it upright again.
Eventually I built my own out of 2x3 rectangle frame stock, with good sized metal casters. I can put a Chrysler 440 on it with full accessories and it doesn't droop at all and rolls easily. Engine stand is one tool you definitely want to spend some money on - buy quality casters and weld one up or have a welding shop make one for you. Will last a lifetime and worth every penny.