Hello Cho,
>> However, we observe that inbound traffic to sites are not fairly load-balanced most of the time so that one circuit hit the maximum bandwidth for the inbound while the other circuit stays less then 50% utilization.
load balancing is flow based meaning that packets belonging to the same flow ( same IP source same IP destination) all follow the same path. This avoids out of order issues.
However, if among the traffic flows some of them have high traffic volume the behaviour can be the one you see.
The proof that the SP is load balancing over two links to each VRF site is given by the fact that both links are used, but you cannot expect an exact load balancing as few high traffic volume flows are enough to have a link more loaded.
Hope to help
Giuseppe