Remember that F-111B was ~85klbs MTOW, not the 100+ of the USAF versions.
Also, even a "heavy" load of say, 10x AMRAAMs and 2x AIM9s is only 4000lbs. Nobody has said how heavy the AIM260s are, but I'll go with ~400lbs for them, to allow F16s to continue using BVRAAMs on their wing tips. It's conceivable that they'll be 500lbs each, Sparrow weight, due to high density propellants, which would make the BARCAP mission load 5500lbs.
Means that a ~42klbs empty fighter could have ~35klbs of fuel onboard!