We debate this often. Many synapse do exhibit learning that looks like weight change, yet there is lots of data that suggests weights are not that important.
First when Hebbian learning was first proposed no one believed that new synapses were forming. It is now known that up to 40% of the synapses on a pyramidal cell can change on a daily basis. Some synapses are permanent and others come and go. Second, individual synapses are stochastic, the amount of neurotransmitter released varies dramatically, sometimes none is released. This says to me that any theory of cortical function can’t rely on any accuracy of weight in the synapse. I once read a paper that studied Hebbian plasticity (sorry I don’t recall the author). One of the observations in the paper was that Hebbian learning seemed more to increase the “permanence” of the synapse than how much transmitter it released. Combining all these led to our model.
It may be that synapse weight may play a role but from a modeling point of view I haven’t seen a need for it.