Well, there are two "weight" limits in the game:
1. The obvious one: the sum of the weight of the items "carried" (by raft, punt, cow, dog,...). A raft can carry a lot of logs, so that's not really a factor for a raft.
2. The surprising one: the number of stacks carried. The PC has a higher stack capacity than the rest. I don't know the exact numbers. If the raft is "overburdened", pick up the stacks one after another until you can move the raft. Start with the lightest stack to reduce the number of stacks on the raft while minimizing the carry weight on the PC.