6. If the three-digit number $\overline{b b c}$ is divisible by 7, and $a$, $b$, $c$ form an arithmetic sequence with a non-zero common difference, then the number of such integers is ( ).
(A) 4
(B) 6
(C) 7
(D) 8
6. D.

Let the three-digit number that satisfies the condition be
$$
\overline{(b-d) b(b+d)}=111 b-99 d \text {, }
$$

where, $0 \leqslant b<9,-9<d<9, d \neq 0$.
$$
\begin{array}{l} 
\text { By } 7 \mid(111 b-99 d) \Rightarrow 7 \text { divides } (b+d) \\
\Rightarrow(b, d)=(1,-1),(2,-2),(3,-3), \\
(4,3),(4,-4),(5,2),(6,1), \\
(8,-1) .
\end{array}
$$

Therefore, all the three-digit numbers are
$$
210,420,630,147,840,357,567,987 .
$$