1. It can mean either. That depends on the context. In your excerpt, the fact this is said while looking straigtht in the eye strongly suggests it is about love.

2. No. With many adverbs the meaning is almost always "to like", but there are exceptions where the meaning is context dependant, like in 1., and sometimes to love is almost the only possible meaning, e.g. :

Je t’aime aussi¹

Je t’aime confusément, secrètement

Je t’aime encore

Je t’aime éperdument, infiniment, passionnément…

¹ Interestingly, this sentence, like its English counterpart, "I love you too" is quite ambiguous. It can mean at least: "I love you just like you love me", "I love you just like I love someone else", "I love you just like someone else loves you" or "In addition to something else I feel about you, I love you"