Disclaimer: I'm a Blockstream co-founder and the primary author of the SegWit proposal.
I believe SegWit benefits everyone in the Bitcoin ecosystem. It solves several long-standing problems that hurt future evolution and scalability:
- Transaction malleability complicates multi-transaction contracts
- Lack of script versions makes introduction of new opcodes complicated
- O(n^2) signature hashing makes worst-case block validation unnecessarily costly
- Lack of input amounts in signature hashing complicates hardware wallet design.
As a side effect, it also gives a moderate capacity increase without forcing the whole ecosystem to adopt new consensus rules, and improves the incentives for UTXO growth going forward.
More information about the benefits can be found here
Of course there are costs as well. They are mostly related to the size of the change. However, it has been a community effort with dozens of contributors that reviewed and tested the changes over the course of several months, with deployments in several test networks, later the Bitcoin testnet, and eventually adopted in Litecoin. A large part of the ecosystem has indicated support or readiness for SegWit.
More information about the costs can be found here.
So to answer your questions:
How would it affect miners except, asicboost?
I don't know. Given the level of industry support, I don't know why they would be opposed to it except for political reasons. The only thing I can come up with is that a sudden increase in capacity may temporarily reduce fee income, but that is expected for any kind of capacity increase.
How would blockstream (other than miners) kind of companies benefit from it, in such a way that miners can't?
Blockstream has no direct business interest in seeing SegWit activated. All its own products (including Elements and Liquid) have had SegWit-like systems built in for years, and work fine with or without it being available on the main chain. Blockstream pays me and others to work on Bitcoin development, including SegWit and Lightning, because it believes that is valuable to the ecosystem we all depend on.
There are other companies that may have a direct interest in SegWit. This includes wallet providers who pay transaction fees for their users, especially multisig wallets, as the benefits of SegWit are largest for those. Hardware wallet creators may like SegWit because it simplifies proving the amount of fee paid to the hardware. Companies whose business model relies on payment channels (which doesn't include Blockstream) may depend on SegWit activating in the near future.