Gunboat diplomacy as an escalation ladder

Did Britain pressure smaller states in the nineteenth century rather than occupy them outright?

Yes. Britain often escalated naval visits from a sloop to cruisers and larger forces, using the threat of bombardment before resorting to an attack.

Gunboat diplomacy used a graduated sequence rather than immediate occupation: a sloop might visit first, followed by a cruiser and then a stronger naval concentration. The ships made coercive power visible while leaving local authorities an opportunity to meet British demands. If that pressure failed, threatened or actual bombardment could follow. The system was bullying, though its visible stages differed from modern coercion that may move more quickly from diplomatic warnings to missile strikes.