Why does force cause a change in acceleration rather than a change in mass? $F=ma$, so force and acceleration are directly proportional.  Force and mass are also directly proportional. Observationally, force alters acceleration and mass is constant but the equation itself does not dictate that the mass must be constant.  Is the answer just that the math is meant to describe the observation and that's just how it is?
As a side note, when a new equation is discovered, how would you know what is variable and what is constant without just making an assumption?
 A: It actually is implied in the formula you stated that mass is constant with time. Newton's original formulation for his 2nd law is:
$$\vec{F} = \frac{d\vec{p}}{dt}$$
Where $\vec{p} = mv$, i.e., momentum.
Putting it in the form of $F = ma$ implies that mass is constant with time.
About your second question. I imagine relationships between variables are supported by experimental evidence. You try and change only a single independent variable and see how the dependent variable changes as a result.
Alternatively, you can work with constants and variables already known to reformulate equations into more illuminating forms or tease out relationships. However, my impression is that purely theoretical results still require experimental evidence to be treated seriously by people.
A: Welcome to physics SE! $F=ma$ is not the fundamental form of Newton's second law, but force equals rate of change of momentum. To get $F=ma$we assume mass is constant. If you want to treat a problem with a varying mass like a rocket you start from the more fundamental form.
A: 
$F=ma$, so force and acceleration are directly proportional. Force and
mass are also directly proportional. Observationally, force alters
acceleration and mass is constant but the equation itself does not
dictate that the mass must be constant.

This is partially true - we observe that there is a quantity that is preserved and that this is a resistance to change in motion (mass). There are actually two notions of mass, inertial and gravitational. It's been observed that these two quantities are always equal, and these give us information about an objects willingness or unwillingness to change. This can help you understand why it might act as a constant - it's really weighting how much the motion can or can't change.

Is the answer just that the math is meant to describe the observation
and that's just how it is?

I personally believe the math is the root of things in physics, not the other way around, so it's good to question what the math means. You can ask different types of physics enthusiasts to get different opinions.

As a side note, when a new equation is discovered, how would you know
what is variable and what is constant without just making an
assumption?

When you are looking into theory, you have to understand what each quantity "is", meaning what its form is. In $F=ma$, the theory is formulated such that $m$ is a constant, and $a$ is the acceleration vector, meaning $F$ must be a vector. You can also track things through the math. For instance, I just said that given that $m$ is a scalar, and $a$ is a vector, $F$ also must be a vector.
It's worth noting that actually what you are learning is the nonrelativistic limit of physics. If you look at more advanced and more complete forms of physics, mass actually can change, and this is treated in relativity courses where mass becomes more synonymous with energy. Also, in general relativity, acceleration is the root of forces, not the other way around.
