Okay so after looking at the damage outputs for unridden vs ridden Lloids it occured to me that they looked like the product of multipliers.
Unridden standard lloid deals 7% early, 5% late. Ridden standard lloid deals 16.1% early, 11.5% late. The percent growth for each pair of values is a flat 130%. To put it one way, Villager adds a ×1.3 multiplier to the damage.
Liftoff Lloid deals 5% early, 8% late when not ridden. It deals 12% early, 19.2% late when manned. Again, both pairs of values have an integer percent growth. This time, damage is ×1.4 of unridden.
Pushy Lloid is sort of tricky, since it's basically impossible to accurately test the base damage of the weak hits given that they are in groups of 4 and nearly inevitably lead into the explosion. That being said, the best estimate I can give for the weak hits without Villager is 1.5%, and 1.75% with Villager. The percent growth in this case is an odd 16.67%, or ×1.67.
What (may?) discredit this is that when I was manually estimating launch angles for the ridden Lloids, they had different angles compared to the unmanned hitboxes. Unridden Lloid has launch angles of 55° / 361° according to mastercore, but with Villager on, this changes to roughly 30°, regardless if its the early hit or late hit (I compared at 999% against known 30° hitboxes). Similarly, Liftoff Lloid has a launch angle of roughly 45° with Villager on, compared to the flat 60° of either the early or late hits without.
Idk, just some super late night/early morning thoughts.
Edit: At the beginning of certain subactions within murabito_claybullet, there is a unk_1BB(1.300000, ). Might possibly be related? I'll test liftoff lloid into higher percents tomorrow to see if the multiplier is actually closer to 1.3.