That sounds like watered down fuel. If the boat is new, find the location of the fuel tank vent. See if it was placed in an area that could be exposed to water as you come off of plane. It's not uncommon for the vent to be placed too low in the splash well or near the transom where it becomes submerged during launching on steep ramps and/or the wall of water that washes in when dropping off of plane. A quick test by taking a fuel sample in a glass jar will rule this possibility out or confirm it. If the fuel is good (make no assumptions), the engine will need to be hooked up to a computer for diagnostics.
The description of the primer bulb is normal. Since the pressure point changes from the bulb to the fuel pump once the engine is started, the primer bulb will lose some of it's firmness as it transitions from a high pressure to a low pressure. The bulb will firm back up with a squeeze as you re-pressurize the fuel from the bulb to the fuel pump.