Although you place your bags on the scale very often the weight is not computed. It is common to use notional weights for passenger bags. If the flight was a charter flight it would probably have been in the order of 13 Kg. Of course your bag (like mine) is probably well above that, but averaged out over a full load that is the figure they come up with.
sometimes actual weights will be given or requested, and the weight divided by the number of bags ought to generate a sensible sort of cross check figure (usually 12 to 18 kgs).
A 757 FUE-LGW would typically have a ZFM of around 80,000kgs and a fuel load of 20,000kg giving a take off mass of (give or take a couple of tonnes) 100,000Kg. If there were an error of 2500 kg or 2.5% the difference to the take off speeds would only amount to about 2 knots (V1. VR and V2 ). given the inherent safety factors built in to the calculations the effect would be negligable., although I am not suggesting it would be unimportant !
many aircraft including the 757 use an assumed temperature method of reducing the take off thrust (by up to 25%) where runway length exceeds that required for a full power accelerate / stop distance. This is achieved by telling the thrust management computer that it is in fact warmer than ambient temperature. The maximum input for assumed temperature is around +54c . So as you can see 28c still leaves a lot of room for derating.
An engine failure after V1 would result in the application of maximum thrust on the other engine in any event and the aircraft would still be around 13000kg under its max certified take off mass in any event, and even then that would not take into account any safety margins built into the performance factors.