The Sakadagami still has some sensual desire; his chains to the world have been weakened but they are not yet broken. But because he is upright and astute in conduct, he will not go to the animal or hell realms. He returns to Earth as a human once, whereupon he makes the effort to finally purify himself of sensual desire.
As for "How weakened are his desires?" I would say they are weakened enough that one more life of practice will completely destroy them. That's all that matters.
Gain and loss, status and disgrace,
censure and praise, pleasure and pain:
these conditions among human beings are inconstant,
impermanent, subject to change.
Knowing this, the wise person, mindful,
ponders these changing conditions.
Desirable things don’t charm the mind,
undesirable ones bring no resistance.
His welcoming and rebelling are scattered,
gone to their end,
do not exist.
- Lokavipatti SuttaStuff I write about things.