Weak subjectivity is a property that innately afflicts Proof-of-Stake consensus environments in that all nodes on the network rely on other node to define the state of the network at any given moment.
In Proof-of-Work environments, all the network nodes retrieve the state of the network through the mechanism itself (by looking at the ledger). Therefore all node are “subjective” to the state of the network (which is strong). On the other hand, in PoS enviorments the network nodes must rely on other nodes to fetch information about the state for them. Here the “subjectivity” is between Node-Node (which is weak). Why the subjectivity model is classified as strong or weak is because in the strong version the entire network (thousands of nodes) must be corrupt in order for malicious activity to take place; while in the weak version a single corrupt node (1 node) is enough to falsify activity.