the bitcoin fee you have to pay depends of the number of bytes of the transaction ( and seems to be independent of the amount of the transaction)
Yes that's right that the transaction fee will depend on the number of bytes on your transaction
but when you perform a sending transaction in blockchain the number of bytes is not displayed so you don't know the number of bytes.So you don't know how much fee you have to pay.
Well that's one of the disadvantages of using blockchain.info wallet and in the end, it might be your fee is too low for the size of the transaction and sometimes it's too huge that's more than the size of the transaction. That's why I'm always recommending using Mycelium wallet because (i) you can see the size of your transaction in terms of bytes, (ii) you can see the size of your transaction fee (per byte) and the estimated time when it will confirm, (iii) you can see the overall transaction fee in terms of (mBTC). The only thing is you can you can't enter your transaction manually, you only have to choose its dynamics fees from priority, normal, economic and low prio but it's still okay for me tho.
Here's some screenshot shot from my mycelium.