It's not worship it's veneration which comes from the Latin word "Veneratio" which in the context we use it means "Reverence" as in "Respect". The honoring of Icons was confirmed as a holy and rightful practice by the Second Council of Nicaea (787). Which restored the Icons after an Iconoclast movement sought to destroy them. This same Council declared in defiance to the Byzantine Emperor that:
"As the sacred and life-giving cross is everywhere set up as a symbol, so also should the images of Jesus Christ, the Virgin Mary, the holy angels, as well as those of the saints and other pious and holy men be embodied in the manufacture of sacred vessels, tapestries, vestments, etc., and exhibited on the walls of churches, in the homes, and in all conspicuous places, by the roadside and everywhere, to be revered by all who might see them. For the more they are contemplated, the more they move to fervent memory of their prototypes. Therefore, it is proper to accord to them a fervent and reverent adoration, not, however, the veritable worship which, according to our faith, belongs to the Divine Being alone — for the honor accorded to the image passes over to its prototype, and whoever adores the image adores in it the reality of what is there represented."
There is also archaeological evidence for this the earliest of which being a Marian fresco found in the Catacombs in Rome where the persecuted Christians under Nero worshiped.