Why is my transaction so big and thus so expensive? I have a bitcoin wallet that I am accessing using Electrum. In this Wallet, I have received Bitcoin from a total of 29 (very small) transactions. Now, I want to access my BCC in this wallet. Therefore, I want to transfer all the bitcoin to another wallet. However, the transaction has 29 inputs and is 4kB in size, making it super expensive!

The suggested transaction fee when using the smallest suggested fee is almost 10% of my bitcoins and thus more than I would earn from the BCCs! Is that normal? Is there anything I can do to circumvent this?
I think you answered your own question.  Yes, the transaction is so expensive because you are combining multiple inputs.  This makes the transaction high in terms of bytes, but low in terms of value.  As such, the transaction fee (which is based on bytes, not value) may not be worth the transfer you are attempting.

However, since it sounds like what you are actually trying to do is access the BCH (Bitcoin Cash) that you also own due to the fork, you can instead leave your bitcoin where it is on the main Bitcoin blockchain, and instead perform your transfer on the Bitcoin Cash blockchain where the fee will likely be cheaper.  This is, of course, assuming you need to move your bch at all.  Unless you need to spend it, you can just leave your bch where it is as well.