Amorously tells you how something is done: in an amorous way. She smiled amorously; they looked at each other amorously. Same meaning as amorous — sexual or romantic desire showing in the act — just the adverb form. It still feels a little dressy and old-fashioned. In ordinary speech you might say “she looked at him with desire” or “they were all over each other.” Though actually, if you only mean warmth or care, that is lovingly, not amorously. The -ly does not make it a softer, kinder word; it keeps the same heat.

含情脈脈地；情慾地