Fitbit integration questions

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Few questions... First off, I have been losing 3 or so lbs per week pretty well. I had thought I was rocking a 9000 or so weekly deficit, and my results would back that up. Normally, I would have my expected calorie burn along with my workouts.
Today is first day with fitbit, and it's adjusting me to 1000 more calories available to hit my goals (which I know maxes out at 2 lbs per week). But, if this is he norm, either I can rock 1000 more calories a week to lose 2 per ( which would mean I am probably closer to a 16000 deficit weekly now (seems unlikely), or fitbit is waaaaaay overestimating my burn. WhIch is more likely?

Question two. I have mapmyrun and fitbit linked to MFP. If I go and do a 700 cal run, it will log in both fitbit and mapmyrun. Will that then double up in MFP as far as activity tracking, or will fitbit just override the mapmyrun numbers!