As one transaction is quite big (I read something around ~4kb), are there any ways to lower that size or is it not possible due to the architecture?
By far the largest field in the transaction is the 2187 tryte signature/message field. Signatures for addresses of security level 2 are 4374 trytes long so actually have to be split up across two transactions; this is part of the design. IOTA signatures are larger than Bitcoin signatures due to IOTA's use of Lamport signatures to gain quantum resistance. It would be possible to further split signatures up between multiple transactions, but this wouldn't actually decrease the amount of data being transferred.
All of the other fields in the transaction are also important. In other words, it doesn't seem likely that transactions will decrease in size, in fact it is more likely that their size will increase to accommodate further features, such as the recently-introduced
Iota transactions are 1.65 kb. So they are smaller then you said. Even if there are any chances to make them smaller by using a diffrent Signature, this would also decrease the capability to transfer data. Data transfer is one of IOTA's main applications, so lowering transaction size, would probably kill IOTA.