I have TableA in a many-to-many relationship with TableC via TableB. That is,

TableA       TableB           TableC
id | val     fkeyA | fkeyC    id | data

I wish the do select sum(val) on TableA, grouping by the relationship(s) to TableC. Every entry in TableA has at least one relationship with TableC. For example,

TableA
1 | 25
2 | 30
3 | 50

TableB
1 | 1
1 | 2
2 | 1
2 | 2
2 | 3
3 | 1
3 | 2

should output

75
30

since rows 1 and 3 in Table have the same relationships to TableC, but row 2 in TableA has a different relationship to TableC.

How can I write a SQL query for this?