I would like filter spam in a way that people have to pay a very small amount of bitcoins to prioritize very good things or to kill very poor things, to make less casual environment and to encourage good filtering. Later best filterers could be rewarded with bitcoins. Is this possible or does this bloat the chain?
Using Bitcoins as a reward and micropayment system is possible. You wouldn't want to send a separate transaction for each micropayment (fee/transaction ratio would be quite big), but you can pay everyone down to a couple decimal places for each operation they make say, once a day. Details of implementation would vary, depending on what you want to do exactly.
As I understand it, as the size of a block increases above particular thresholds, the transaction fee required to include another transaction in a block goes up. This is by design to prevent bloating of the blockchain.
This would mean that trying to include many small transactions in a short period of time would either result in large transaction fees or delays in transactions being confirmed.
Even though Bitcoin is commonly spoken of as being great for micropayments, I don't believe that's literally true if you consider a micropayment to be in the order of a millionth of a bitcoin (micro meaning a millionth). Maybe it would be better said that it's great for millipayments?
A very similar idea already exists, see http://www.hashcash.org/. It requires proof of work to be send with every message, so spammers are paying by cpu-cycles.