How does Caesar calculate how much fluid weight goes to each support? I'm asking particularly in regards to tall risers that have intermediate supports. My model seems to be showing that the weight of the fluid is distributed amongst all the intermediate supports instead of pooling at the base. Does Caesar assume that a rigid anchor stops fluid from falling through a pipe?

I have a 10" riser 610 ft tall carrying water inside a building. We are using gapped Victaulic flex couplings every 10 ft to handle the thermal expansion. Per Victaulic recommendations, this means I have an intermediate anchor on the pipe every 20 ft (2 couplings between each anchor) to control the piping. At the lower base el, I'd expect the anchor to see total water column fluid weight (17.4 kips) + pressure thrust (27.2 kips) + the weight of piping between the lowest intermediate anchor and the base el (1 kip) for a total of 45.6 kips vertical load. At the intermediate anchors, I'd expect the pressure thrust to cancel out, and only support the weight of pipe between the anchors (0.8 kips). Instead, Caesar is telling me I have 25.5 kips at the base el and 0.9 kips at each intermediate anchor.

Loads are associated with each element. The fluid density defined for the pipe element develops load on that element alone.
This works well in most models but you highlight an issue will tall risers.
Think of the fluid as "sticky" - it sticks to the pipe and does not seek the lowest point.
Note too that fluid head does NOT change pressure. Your input values for pressure (P1, P2, etc.) are used directly.
Also, watch out for pressure thrust loads on (untied) expansion joints. We place a thrust load on either end of the XJ rather than at those up- and downstream surfaces where the pressure loads are truly located. There are many posts here on this topic.

Thank for the clarification Dave!

Note that typical current practice is to select a pressure for CAESAR analysis along the entire line that matches the highest pressure and highest temperature (and in the case of cryogenic systems, lowest temperature) seen anywhere in the line.

So if you have a hydrostatic head at the bottom of the pipe, plus static pressure, you have a design pressure with which to select a wall thickness or piping specification. That pressure then in turn gets fed into stress analysis, and is applied to the entire line in most cases.

In most cases, this is conservative, but when you have thin-walled bends, pressure differentials may result in differing elbow stiffnesses and SIFs and therefore inaccurate results.