If you look at the transaction in question:
  https://blockchain.info/tx/2282f8922119c3d6900450695af0926dfeaba4e3818ebf93d5c60ac15e9183f5
you see that a fee of 0.001 BTC was given to the miners.

Blockchain.info themselves didn't get anything from you - but for some reason their wallet decided to pay around 10 times the usual fee of 0.0001 BTC.

I don't use their wallet myself, but seem to remember they have a setting for how much fee to include. Did you perhaps select the "generous" setting? I can't think why else they would include so big of a fee.

Note, by the way, that fees are pretty much constant, no matter how much value you are sending. A fee of 10 cents to send 30 cents worth of coins sounds very expensive, but if you were to send a million dollars worth of coins, the fee would still be just 10 cents. It takes the miners the same amount of work to mine a 30 cent transaction as it does for them to mine a million dollar transaction, and they both take up the same amount of space in the blockchain too - so they cost you the same in fees (roughly speaking - sizes and fees do vary based on how many inputs the transaction consumes, and various other factors; there are rules about compulsory fees for sending small amounts to prevent people from sending thousands of tiny "spam" transactions and blocking up the pipes, too).

Edit: See this transaction in which I sent 38,000 BTC without paying any fee at all.

Edit2: About your privacy concerns: while it's true that everyone can see the "balance" at any given Bitcoin address, if you don't tell us which addresses you own, we won't know how many coins you own. Blockchain.info's wallet has the nasty habit of reusing the same address over and over, but if you make a new address for each transaction you do, it becomes harder for people to connect "TonyT" to the blockchain. We'll be able to see coins moving from address to address, but we won't be sure which addresses belong to you.