In English grammar "weak" verbs are those that have regular "ed" endings in the past tense; "strong" verbs are those that have irregular endings. But these terms are now commonly used to denote inferior and superior verbs. The concept has developed that some verbs are more forceful that others because they are "strong," but is this a misreading of the grammatical definition of weak and strong? Obviously one should try to find the most exact verb for a construction, but are there really verbs that are inherently "weak" or "strong" outside of the strict grammatical definition of "weak" and "strong"?
People on writing sites speaking of "strong" and "weak" verbs are not speaking of any sort of scientific or objective classification. I doubt their use of the term strong even originates in a misreading of the grammatical definition of Germanic strong and weak verbs (as you suggest).
They're simply using the word strong with its lay meaning, "forceful," rather than its technical meaning. The technical, objective meaning is pretty much irrelevant for creative writing advice. The word "strong" is just used to reference the writer's feeling or intuition that some verbs have a stronger mental effect than others. Example here: http://theunnovelist.com/super-verbs/ Note how it describes the listed verbs with a variety of adjectives: "super," "strong," "active," "creative" and "precise." None of these adjectives are used here with a very definite or precise meaning: they're just meant to make the reader think "these are some really good words to use in my writing!"
A common metaphor on these kind of sites is that good writing is "strong" or "vigorous" or "muscular" or "active" while bad writing is "weak" or "passive" (that last one is unfortunately prone to confusion with the grammatical concept of voice; see "How long have we been avoiding the passive, and why?" and "Fear and Loathing of the English Passive"). There's a whole body of received wisdom among creative writing gurus about which kinds of words and constructions are inherently "strong/active" (not in the grammatical sense) and which are inherently "weak/passive." For example, these kind of websites also often deify nouns and verbs as the "strongest" parts of speech, and condemn the use of any other parts of speech (especially adjectives or adverbs) as a necessary evil at best. Ranking verbs against each other (ignoring any possible effects of the context) just seems like another example of the same mindset.