For seriousness and solemnity:
* Seriously
* Solemnly
* Earnestly
* Severely
* Somberly
* With gravity
For danger or illness:
* Dangerously
* Critically
* Seriously
* Precariously
* Perilously
* In a precarious state
For a deep, low voice:
* Deeply
* Hoarsely
* Resonantly
* With a low voice
For slow and deliberate:
* Slowly
* Deliberately
* Steadily
* With care
Please provide more context about how you're using "gravely" and I can give you more specific synonyms.