The damage bonus is represents the amount of momentum you are throwing into your attacks; the speed that your strike is being done with (Strength) and the amount of mass you have going behind the attack (Size). A physically weak person who lacks strength relies more on their body mass than their strength to put force into their attacks. That's why you can't do damage bonus without the size stat in any reasonable way.
Size also adds more strategy to the game. A creature that has a significantly more size than your character is dangerous in close combot, but less so in ranged combat (most projectile weapons in BRP either don't recieve damage bonus or only half the damage bonus, not all though) . This prevents fights from turning simply into a bunch of boring rolls and instead takes on greater dimesions. It encourages players to fight using their environment. It encourages them to actually think about what weapon they want to fight with.
The size stat also serves as a conveniant means to comparing characters in the game. A monster with a size of 20 is twice as big as a character who is of size 10, and the numbers go up as high as you can count. The small, medium, large, and huge system tells you if something is bigger than you, but not how much bigger, and after you reach huge, thats the end of it. That means that in that system, a living planet is in the same size category as an elephant, which is frankly stupid.