Liquid sterling doesn't like to go where it's 'cold', so if you
don't heat the wire above where you want the bead, the wire won't
melt properly. Also, make sure the tweezers are not too close to the
end to be melted; they will act as a heat sink and you'll just wind
up with damaged sterling and no bead.
The analogy I use with my students is, "You don't want to get into
an ice-cold bed, do you? So warm it up first."
16g is pretty stout stuff for making a bead on a wire. There's a lot
more mass than say, as 20g wire (shepherd's hook type earwire); the
heat energy required is MUCH larger. You don't really need a hotter
flame, just more volume of heat into the wire. If you don't overcome
the heat capacity of silver, your results won't be good even with a
very hot, focused flame.
I would hold the fluxed wire two or more inches away from the target
end. "Dip" the wire into the flame once or twice to get sufficient
heat built up into it before concentrating on the end to be melted.
(I use acetylene/air, and I use the 'width' of the flame as my
guide...dip at least the length of wire into the flame that equals
the width of the flame.)