what is you cpu freq.? You've set TWBR=1, which would mean that i2c clock would be very fast, 888kHz? Prescaler is 1?
I have too much capacitance on bus, I had to go with 48.
I can confirm, that is works with si7021, this would then also work with si7051.
But would like to ask, if 278 for Vcc is correct? as far as I know you are looking at bandgap voltage, right?
Any reason you are going for "everything done fast as possible"?