Arial Black
Adventurer
The rider won't stack with itself. If he takes the Booming Blade damage initially as he's moving around (before he goes out of your reach and triggers an opportunity attack), then that's fine and it works--but if he hasn't, then even if you hit him, all you're doing is renewing the "booming energy" around him (whatever that is). You don't double the rider, because spells don't stack with themselves. If you're 10th level, he'll take 2d8 damage when he moves, not 4d8.
So, if the same PC is hit by two fireballs from the same caster, he only takes damage from the first?
In this example, the victim has been hit by two castings of the same spell. If the spell in question gave you, say, a constant bonus of +1d4 to damage for one minute, then the +1d4s would not stack to make +2d4s if you cast the spell twice. The weapon either makes the weapon do +1d4 damage, or it doesn't, no matter how many times you cast the spell.
But if the spell directly damages the victim, it's not that the damage 'stacks', it's that damage is done twice.
The question is, does the thunder damage occur when triggered and then end while two castings each do what they say they do (damage effectively 'stacks')? Or does the spell give you a constant effect (of a sonic sheath existing until you move) that cannot stack; you either have a sonic sheath around you or you don't?