A fielder usually is not guilty of obstruction if they have the ball or are in the act of fielding the ball. I say "usually" because if they do something deliberately to hinder a runner they can be guilty of obstruction. Take for example, R2, grounder to F6 who does not field the ball cleanly and is still bobbling the ball as R2 goes by. Since F6 doesn't have complete control of the ball for the tag, he sticks out his foot and intentionally trips R2. That would be obstruction.
In your case, F3 was in the act of fielding the ball and in fact did have possession of the ball at the time the BR slowed down. Since F3 did nothing to deliberately hinder the BR, there can be no obstruction. In fact, if the BR had collided with F3 while she was attempting to gain control of the ball, I believe that you would have had interference on the BR.
The double base is intended as a safety measure, but its presence doesn't annul the rules. If the fielder has possession of the ball, then they can legally block the runner's path to the base, even if the base is the double base.
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