"Ok, there should be a tension
"Ok, there should be a tension screw that will allow you to tighten it up a bit.
Looking at the motor as if it was hangin' on the boat and you were on-board.
Just under the lower cowl on the right hand side (right up near where the bracket meets the bottom cowl) there should be a screw or hex head type bolt - it screws into a kinda raised round dimple (best way I can think to explain it) - it may be slightly obstructed by the tilt locking mechanism.
It pushes on a little plate inside, which then butts up against a plastic bushing that surronds the pivot that the engine turns on.
You can tighten that up to suit. The bushing inside is prone to breaking over time and are a royal pain to get at and change, so don't reef too hard on the screw - just tighten slightly and only go as much as you need to, to get the "stiffness" you are looking for."