Members of the EEA have to accept EU legislation and make payments to the EU and the jurisdiction of the Court of Justice of the European Union. Not full emmbership fees. Also they're part of the decision process shaping EEA policies.

https://en.wikipedia.org/wiki/European_Economic_Area#Rights_...

Another option is EFTA and bilateral agreements like Switzerland. However, the May government decided not to pursue EFTA membership and Norway isn't that keen since thay're afraid it would impact future EFTA/EU negotiations and they could use some of their current rights.