"operated by Air Norstrum" means Iberia rules and the rules from the first flight, which is international and therefore 23kg limit.
If you have Iberia frequent flier status then you can take an extra bag for free.
There is no weight limit on hand luggage and the spanish carry a sh*t load of the stuff, normally 2 huge bags, so you may be able to get a bit in hand luggage. However, Air Norstrum operate ERJ aircraft which have tiny overhead lockers, so you may be limited on this route with hand luggage.
May want to look into either unaccompanied baggage, or using a someone like Shiply.com (a reverse bidding auction). Shiply shipped my motorbike from Gatwick to Jerez for £210, door to door!