Weevil is obsessed with being Whitebeard's "child." If you recall in one of the first appearances with Weevil, he wanted to pursue Blackbeard for revenge, and Bakkins basically shot that down. It'd make sense for Weevil to care about the citizens of his "dad's" homeland, if he felt that his "dad" did.
Ryokugyu doing that is literally par for the course. Not even 20 chapters ago he was threatening Wano's citizens unless they brought him Luffy's head. He's a complete asshole and believes that those not under the WG rule are just NPCs in Grand Theft Auto for him to kill when convenient. I could easily see Weevil struggling against Ryokugyu given the latter's ability being pretty OP, and being faced with going with Ryokugyu peacefully, or risking the lives of the entire island. I mean, the premise to Ryokugyu was Weevil defending the island against marines, right?