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Kiwipic, welcome to the Forum.
For what I remember, there are not a lot of trees where you can hang your hammock. Well, actually there are trees, but you won't find anything with a good space to hang it. It's either too close or either too far. So I thing that the best for you it's to buy a lightweight tent. Or you can take the sleeping bag + bivy bag. If you only take the sleeping bag, at least don't forget about the liner and the mattress.
Just bear in mind about this situation also:
http://www.caminodesantiago.me/community/threads/wild-camping-on-the-caminho-português-allowed-or-forbidden.20903
I think that you'll not have any problem, BUT, you are going on the worst time of the fire season, and Forest Police tend to do a lot of patrolling (at least here in Portugal). After you reach to Spain, the law it's very different for camping. You can't camp in the wild if you are in range of a Camping park ( think it's 3km), you have to camp at least 300m from a big city, and you can't make fire, which means you have to take a camping stove.
I know about people who camp along the Caminho Português, and they seem to have no problems with the authorities, but sometimes it happens you know.
Hope that I've helped you.
Best Regards
Diogo