How much will Segwit *actually* increase bitcoin capacity for realistic transactions?
Note that the scriptSig field is not just the ECDSA signature itself (65 bytes) but also the public key in the case of a P2PKH input, or the redeem script for a P2SH input, and a couple more bytes for sizes. Also, there is a scriptSig for every input, not just one per transaction. You are looking at the average transaction size, most of which contain multiple inputs, but then assuming only one signature of 65 bytes. 

Let's take an example transaction with a single input and output: https://blockchain.info/tx/82d62d5f4e69ae8338c39b7ae2e1d33db59bdf62c869ded7344adc936bab8653

This transaction is 226 bytes, 108 bytes of which is the scriptSig (including the length byte), which is nearly half the size of the transaction. Because the average transaction has more than just one input, the multiple scriptSigs make up a higher percentage of the total transaction size in those transactions - on average around 60% of the transaction. Taking that into account gives you the estimated increase on average, which was based on simulations run with the new rules according to current usage I believe.


  Really weight is a new concept, previously it was measured in bytes.


Indeed, it's misleading to say weight was the transaction size in bytes before this new weight was defined, you should compare the old size to the new virtual transaction size (which basically is what you did anyway by dividing by 4)