What is the formula for determining how much weight (people and gear)
a catamaran can comfortably carry? ($10)

Hallo Harnold,
as this is Physics, you get a textbook answer: the weight any boat can
carry is equal to the weight of water displaced (i.e. shoved out of
the way by the boat). So if your boat is in fact a cube with sides of
length 1 metre, then it could displace a maximum of 1 cubic metre of
fresh water, which weighs 1000 kg. If the cube itself weighed 400 kg
you could load 6 people weighing (with their baggage, etc.) 100 kg
each and the cube would just float level with the surface of the
water.

In the real world you will want freeboard (i.e. a distance between the
water and the deck). Measure the volume of the hull below this line,
calculate how much what the water will weigh if it theoretically fills
the volume (bearing in mind that the density of sea water depends on
where you're sailing) and double this weight (you've got two hulls) is
how much the catamaran with equipment, rigging,  crew, stores, baggage
etc. can weigh. Subtract the unladen weight of the catamaran and
you've got your loading figure.

Calculation of the volume of the water displaced by the hull depends,
obviously, on the shape of the hull. You can try approximating the
hull shape as a half cylinder, which for two hulls equates to a full
cylinder, which has a volume of Pi x radius squared x hull length. Or
you can look in the ships papers - the loading weight should be in
there.

If it is a sailing catamaran, you need also to consider what happens
when it heels and one hull has to bear most of the weight.  I expect
this is why they sit rather high in the water when not sailing, but I
don't know if that means that each hull must have potential
displacement to float the complete weight of the boat and passengers,
etc.