Security when reusing encryption key?

I read in that it is recommended to use a new nonce when encrypting data. For blockstack gaia, each app does only use one nonce based on the domain name, correct?
Does this pactise weakens the security with increase of the stored data sets? If yes, does it matter even more for collections as the structure of the data is known?

The problem described does not appear to be relevant to the ECIES scheme used in blockstack.js. In blockstack.js, a new private key is generated each time you encrypt something (you can see for yourself here).

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