We have more power now! You have a limited power among your people!
The Bayonet Constitution greatly limited the king's power.
The power to fire the Cabinet was given to the legislature, which already included many rich Americans.
The Bayonet Constitution's other purpose was to remove the Native Hawaiian right to vote. The privilege of voting was no longer limited to citizens of the kingdom, but was also given to foreign residents such as Americans and Europeans. In order for Natives to vote they need to show high property or income, which left out 2/3 of Hawaii Natives.