If i have high tire pressure (near limit) and then I load a lot of weight onto the car. Does that mean the chances of my tire being blown out increases? What's the science behind it?

 

Other way around. More loading requires higher pressures to support the load, otherwise the tire flattens & bulges too much, preventing the sidewall from keeping the proper shape to support the load. That is what causes a blowout once the already stressed sidewall runs across/into something that pushes the material past its design failure point.

Explorers were blowing tires not so much because of faulty tire design or manufacturing errors (there certainly were some) but becasue Ford decreased the pressure from 32 to 28 to make the ride cushier for soccer moms. 28 itself is not so much of a problem, but the normal tendency to run with underinflated tires...under the already low spec... was the dominant root cause.
This despite their own engineers and Firestone calling for an increase to 34 or 36 to handle the extra weight over the original Ranger design. A magnificent PR campaign succeeded in turning it against Firestone instead. My 00 Explorer got a new sticker on the door when I had the tires replaced in the recall. Old pressure:28 new:32.

One's tire pressures would have to be far far higher than any reasonable number to risk blowing a modern tire like a balloon blown up too far. Especially if you are loading the vehicle within its listed specs. There is at least a 2x safety margin in almost every product released into the public. Probably more in most cases. I'd be much more worried running 10lb under than 10lb over, in any load condition.

 

The vehicle has a recomended tire pressure but it does not always match the tire pressure listed on the tire.. I always go by the tire manufaturers limits.. The tires going to blow out if you hit something big enough but your just as likely to pick up a nail running low or high....