Is the birth registration, 1877, the only occasion when you see Henry BRIDGMAN, son of Leah BRIDGMAN?
Was he brought up with Leah's children with Richard THOMAS?
How did Leah describe herself on the marriage certificate.........widow?.........spinster?
If she is a spinster you might think that Henry is not with her in 1877.
If Leah is a "widow" that might suggest that Henry is with her in 1877.