Another good example of what the barycenter is like for the Sun is the "teacups" ride at the fair. Orbiting cups which you are one side of, all on a larger orbit, all on another orbit....okay so like a tea cup on a saucer on a plate...stay with me here!

When the planets line up, you as the sun are pulled hard and flung around like the line up of the orbits on the ride, lining up to fling you around the outside at highest velocity, most pull.

When the orbits are spread around (jupiter on one side and most everything else on the other) You are near the center of the combined rotations and the fling is not so great.