Properly set up your bow will shoot many differently spined arrows accurately at ten yards, but only the correct spine arrows for your bow will still hit the same vertical line at 10-20-30-40-50yards. Doing a walk-back tune with too light a spine arrow will show a hook to the left. Too heavy a spine will shoot to the right.
I may be misinterpreting your statement, but if you are testing spine, you should be using a bare shaft. If they are weak they will will fly right. If you're doing a walk-back with fletched shafts, adjustments are usually made to the rest position. Spine tests should be done before walk-back tuning tests are started. Even if you didn't do it correctly, I would still expect the weak fletched arrow to fly to the right, the farther back you go.