It is clear that only addresses can vote, not wallets like one might think after reading the current guide.
That's correct - but as change addresses aren't used by the main wallet software, in ordinary usage one wallet will use only one address.
But when you look through the voting results you can see that multiple actual officers got a vote by an address with a very big amount. The weight of that vote counts different for each of those officers.
Does that mean that the weight of the vote is calculated once, when voting, and keeps like that until a new vote is given?
The result is calculated from the votes and balances as they stood 20 blocks previously. Updated balances and weights are re-calculated every time.
In the 'Supported By' section of the vote report, it looks like the same address has a different balance depending on the vote. This is because some candidates receive greater than the Droop quota (the amount required to win), so the software considers that only a portion of the balance was required to win the vote, and that is the amount shown. It has no impact, and is a vestige of the MC1 voting where more than one candidate could be elected in a single vote.