The distinction between a weak verb and a strong verb is based on how the past tense of the verb is formed.
Strong verbs (also called irregular verbs) form the past tense or the past participle (or both) in various ways but most often by changing the vowel of the present tense form (for example, give, gave and stick, stuck).
In Garner's Modern American Usage (Oxford University Press, 2003), Bryan Garner offers this explanation for the modifiers "strong" and "weak":
Irregular verbs are sometimes called "strong" verbs because they seem to form the past tense from their own resources, without calling an ending to their assistance. The regular verbs are sometimes called "weak" verbs because they cannot form the past tense without the aid of the ending (most often -ed).In fact, the term "strong" has been inherited from Old English grammars, and many of today's irregular forms are descendants of common Old English verbs. Although fewer than 200 modern English verbs are "strong," these irregulars (most of which are just one syllable in length) are among the most common in the language.
For more information about strong verbs, see our Introduction to Irregular Verbs in English.