Lea, Lee and Leigh aren't British versions of the biblical Leah. The languages aren't related at all. In Anglo-Saxon the word (not name) leah meant a grassy field or a meadow, and the -h would have been pronounced in a throat-clearing way! But that -h hasn't appeared in English spelling or pronunciation for centuries. So in modern English all the Lee names mean Meadow and the Hebrew name Leah is completely different in its origins. As for the meaning, it's such an ancient name that nobody knows for sure: there could easily have been several names in related languages or dialects with different origins, which might account for the different meanings put forward. As for "weary", it sounds odd to us but in ancient times people sometimes gave their children names with a negative meaning so that others, especially supernatural beings, wouldn't be jealous of the child and harm it.
I don't know about "the light of the sun" in Gaelic, but I'm a bit sceptical.