If the nut slot is cut too deep, buzzing normally occurs when playing the open strings. If buzzing only occurs when you play the F and F#, this suggests the following possible causes (in my experience):
1. Bad technique - you mention you have weedwackers, these strings are very soft low tension (look transparent) and shouldn't require much 'effort' to get a 'clean' note.
2. There's a bump in the fingerboard - quite likely, in which case, check with a straight edge and get a luthier to sort.
3. Resonance, usually from the endpin inside the body - if this is the case, there should be a buzz when you play F/F# in other positions. If this is the case, pull the endpin further out (or move it further in), which will change the resonant frequency.
Hope this helps