Multibit security — How anonymous is it?
I think what you are asking is this:

Because Multibit is a lightweight SPV wallet, it uses Bloom filters to request the status of its own wallets from other peers rather than collecting the latest blocks.

Could those other peers, who already know the IP address, conclude that the request for information concerning certain addresses imply that this IP address is looking after these addresses?

The answer would be yes it could conclude this, but it could never say for sure if the private keys were also owned at that IP address it could only assume this.

The matter is further complicated because connection to peers is fairly random according to their availability.

EDIT I am updating my reply, as it appears that some research has been carried out which may contradict what was thought to be the case, but this is not strictly related to Multibit, but all wallets that use internet protocol. The Coindesk article points to the paper:

"Eavesdropping" attack