Does weight have the same vowel sound as ei in neighbor?

No, "weight" and "neighbor" do not have the same vowel sound.

* Weight has the vowel sound of "ay" (like in "say").

* Neighbor has the vowel sound of "eh" (like in "bed").

The "ei" in "neighbor" is a diphthong, which means it's a combination of two vowel sounds. It sounds like "ay" in "say" but shorter and more clipped.