We are getting a few terms mixed up here, I feel.
What Jimmy has quoted is the requirements for an aerodrome to be considered a Suitable airport. An aircraft on an ETOPs flight must always be within the ETOPs maximum threshold (120, 180 or 207 mins at the pre-determined, single engine diversion speed as appropriate) at any time that it is more then 60mins flight time from an Adequate airport.
There are no weather requirements for an airport to be considered an Adequate airport.
I think what tayareci might be referring to a Fuel en-route alternate, required to reduce contingency fuel from 5% to 3%. Such an aerodrome need only meet the requirements of an Adequate airport, and as such has no weather requirements.