Old English gesælig "happy, fortuitous, prosperous" (related to sæl "happiness"), from Proto-Germanic *sæligas (source also of Old Norse sæll "happy," Old Saxon salig, Middle Dutch salich, Old High German salig, German selig "blessed, happy, blissful," Gothic sels "good, kindhearted").
This is one of the few instances in which an original long e (ee) has become shortened to i. The same change occurs in breeches, and in the American pronunciation of been, with no change in spelling. [Century Dictionary]
The word's considerable sense development moved from "happy" to "blessed" to "pious," to "innocent" (c. 1200), to "harmless," to "pitiable" (late 13c.), "weak" (c. 1300), to "feeble in mind, lacking in reason, foolish" (1570s). Further tendency toward "stunned, dazed as by a blow" (1886) in knocked silly, etc. Silly season in journalism slang is from 1861 (August and September, when newspapers compensate for a lack of hard news by filling up with trivial stories). Silly Putty trademark claims use from July 1949.
It is a widespread phenomenon that the words for 'innocent', apart from their legal use, develop, through 'harmless, guileless', a disparaging sense 'credulous, naive, simple, foolish.' [Buck]