I wrote an article in a German magazine about 15 years ago about sinew backing.
In the article I stated,
"I disagree with backing a bow with sinew as a remedy for a poorly built bow." (Not to say Coaster, that yours is poorly built.) If I wrote it today, I would add,
"for a bow that turned out light." I also went on to say,
"Backing a bow with sinew should be intentional. It should be done for the purpose of building a special bow with unique requirements. A considerably shorter bow that still allows the same draw length and weight of its all wooden counterpart." I've sinewed a bunch of bows since then and still agree with my statement of yesterday. Again, not that yours is poorly built. More times than not, the "fix" doesn't turn out as you hoped. Sinewing should be part of the plan from the very beginning. What I'm trying to say is, be happy with the bow you just made and chalk it up to experience and learning. To this day, I make bows that come out lighter than I wished for.
It happens. If you just can't stand it, do what I do...give it to a kid.