Back Swing Interference or Play On
 

So from my understanding of the back swing interference rule it exists to help the defense and not the offense. FED rules. Batter swings and makes contact with the pitch and hits a grounder right down the first base line. In his follow through his bat makes contact with the catchers helmet. I have a no call and the first baseman fields the ball and tags first and the inning ends. Neither coach says a word and the game continues. Was I correct?

If the contact happened after he hit the ball when his bat came around then it's nothing unless you believe it to be intentional. Part of the hazard of playing catcher.

FED does not have "weak" or backswing INT. It's either INT and an out or nothing. Judgment call: but if F2 was not fielding the ball, then it's not INT.

For OBR, "weak" INT is called when the batter misses the pitch but makes contact with F2 throwing to retire a runner who is stealing. It's not called on a fair batted ball.