If you look at all of those, they are serious and carry a negative tone- grave news would be a death or suchlike- serious, but grim.
Here's a list of some of the most common words associated with 'grave' (searched at
http://view.byu.edu/ ) and you will see what I mean.
3 concern
46 danger
35 doubts
32 goods
31 foot
29 face
27 cradle
20 risk
13 situation
13 risk
12 consequences
12 problems
11 pauper
10 father
10 matter
9 error
9 expression
9 mistake
9 side
9 threat
9 reservations
8 giant
8 offence
8 misgivings
7 case
7 family
7 head
7 voice
7 war
7 difficulties
6 bottom
6 difficulty
6 discovery
6 injustice
6 breaches
6 charges
BTW, do use this site- it's fantastic for getting more information about a word- you can search a huge database (The British National corpus). Here I asked it for the nouns coming immediately after 'grave'. Do try it- it can help where dictionaries may fall down.