It’s offered by those wishing to include their transaction in the next block. Miners look at all the pending transactions and select the most lucrative ones.

Every block has a limited amount of space for transactions (1 MB previously, 4 and up to 8 technically with segregated witness?) , the person mining the block includes transactions based on fees provided by users initiating the transaction.

If there are tons of people looking to make transactions, fees go up or down based on people's willingness to pay to be included in the next block.

In practice Segwit only increases the blocksize to 1.4 MB for normal transactions and theoretically to 4 MB, but then blocks are filled with special kinds of transactions people don't really use.

It also doesn't really increase the blocksize, but move some data outside of the blocksize calculation to make room for more transactions. The important difference is that Segwit is opt-in and depend on usage for it's effect, while a blocksize increase would immediately increase transaction throughput to its full capacity.

Bitcoin Cash chain has done increasing the blocksize rightfully.

Essentially by market forces. Transactions with too-low fees don’t get added to the chain.