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This shop Alza basically refunds PEB even if the item is above 100g.
The heaviest item I did was about 700g and kinda cheap but someone told me a limit is 1200eur.
The only thing you need to do is sing a declaration on oath (excuse me if I used the wrong term I am translating word for word here)

Anyone can explain why do they refund items right away without cross checking ?
Also is there a chance they check back on all the refs on my accounts and see that weights match ?

If it's something like an affidavit they can take legal action on you if they were to go back and see that you lied about the weights. However, that is incredibly unlikely.

doesn't affidavit have to be signed in front of some legal person ?

Signing online has the same weight as signing in person in the US.