Does anyone understand the difference between weak likelihood principle and strong likelihood principle?
Yes, it's straightforward. The weak LP is within a given model and distribution (it's essentially just the sufficiency principle within a model), whereas the strong LP, SLP, makes the claim (of equivalent evidential import) for pairs of models. Easiest to refer to my paper here: http://errorstatistics.com/2014/09/06/statistical-science-the-likelihood-principle-issue-is-out
fortunately, it turns out the the SLP does not follow from sufficiency and conditionality, as had long been thought.