I've looked and did some research and science on unit mass. Here are my findings.
Using KGCM, I took a unit with 1.2 mass (Rhyfelwyr) and made it charge into a unit with just 1 mass (Ceitherne).
1st test: 1 vs 1.2. No horizontal push, so mass has no or marginal effect in combat.
Then I started making modifications to the Ceitherne, so it has less mass.
2nd test: 0.8 vs 1.2. No horizontal push, mass has no or marginal effect in combat.
3rd test: 0.6 vs 1.2. Little to no horizontal push, mass has no or marginal effect in combat.
4th test: 0.4 vs 1.2. Some horizontal push, mass has an effect in combat.
This is where the science comes in, and I try to find out an exact number on where mass starts to have an effect on charge. Turns out it's around 3.07 or 2.97 times the defending units mass, give or take. So if it's less than that, there'll be no horizontal push. In order for there to be vertical push, the unit has to have the launching trait or be a cavarly unit, which then the launching will occur when the charging animation collides with the unit.
Beyond the mass differences of 3.07 and 2.97, it likely adds the difference in mass to further horizontal push, just like real physics. Same likely goes for launching push.