Specifically, I am trying to wrap my head around this scenario but can't do so solely by thinking about the weight of the fluid.
Imagine a perfectly still lake. If you dive into the lake, the further down you go, the more pressure you feel – presumably because of the weight of the water above you. Now, imagine that I replace some arbitrary chunk of water beneath the surface with a (rigid) solid object that is magically held in place. If I were to swim and place myself beneath this object, one would naively think that there is less weight of water above me (after all, we got rid of some chunk of fluid), but in fact I feel the same pressure on me regardless of whether the object is there or not. In essence, it's the height I am beneath the surface that matters, not the weight of the fluid above me. Why? What is generating this force if not the weight?
Best Answer
The concept you need to include in your thinking is related to Pascal's Principle. As applied to your question, it means the pressure from the water above a particular position under water does not just act downward. That pressure acts in all directions. So, in effect, pressure in a fluid "moves around corners". When you are under the hypothetical fixed object in your scenario, you feel the pressure from the water to the sides of you. That water feels pressure from the water above as well as to the sides (and bottom) of it. If more water is added, or you and your object are deeper, the greater weight of more water above the water to the sides of will result in greater pressure there which will be transmitted in all directions including toward you.
Another way to look at this is if the pressure were less under the object, the greater pressure on the sides would "push" more against this lower pressure region until the pressures were equal.