It should not have to be a light load. If the hooks cant take an side load equal to what they can take straight on then they are substandard or improperly installed. Sorry but it's true and I'm not going to argue it.
I had my Terex 640 14 yrs using the hooks the same way, even lifting the rear off the ground many times against a chained load. Very heavy 14k pound tractor - no hook problems.
Not according to even basic high school physics, nor does your anecdotal lack of hook problems prove any theory. They were clearly substantial enough for what you were doing, even when side loaded. By the same token, I've had a middle hook on each of my last two machines, with no issues. Equally irrelevant to the argument.
Simple premise: the weld and supporting material around any side-loaded hook is going to handle a very small fraction of the force it can handle straight on. Not only that, but the geometry of most hooks, thicker in lenghwise axis than across, favors a straight-on pull. It is a simple lever length/torque problem, Archimedes figured this out 2400 years ago.
Not only that, but lifting with center-loaded chain on dual side hooks actually multiplies the side force on the hooks, by the angle of the dangle on that center chain. This is why a 200 lb. man can easily deflect a cable under 10,000 lb. tension, when pressing in the middle of the span. If you're going to pull with a side hook you're much better off just hooking to one, or making the chain between them long enough to minimize the side loading.
Of course, it's likely better for your loader to pull on-center, which is why many of us just have a center hook.
@ovrszd had it right, guys.