In many species, females will only mate with males who come to them bearing gifts. Males who don't deliver the goods are rejected, and males bearing small gifts may only be given a short time in which to copulate.
In the case of balloon flies, the male offers the female a large white balloon. Original research was carried out on this by Kessel in 1955
Like many evolutionary sequences, this ritual seems to have become more complex over evolutionary time. Other species of the same family of dance flies, the Empiidae, to which the balloon family belongs, display mating behaviours that seem to point in the direction of the behaviour shown by the balloon fly.
Some species mate in a haphazard manner – males approach females, who sometimes mistake them for prey rather than potential mates and eat them – the ‘pick her up in the pub and risk getting your face slapped’ approach.
Other species avoid this hazard by distracting the female by offering her a prey item and then mating with her while she is consuming her meal – the ‘take a bottle of wine to her house while she cooks you dinner’ approach.
Some members of the species Hilara wrap the prey item in silken threads in order to subdue it before presenting it to the female – the ‘take her out for a slap-up meal’ approach.
More advanced members of the species Hilara create a complex silken balloon that is either empty or contains a piece of vegetation - the balloon itself becoming more important as a signal of courtship – the ‘give her expensive gifts’ approach (because the creation of the silken balloons takes it out of the male balloon fly, reproductively speaking, as it consumes a lot of energy).
Males can lose a lot of their mass in producing these gifts. Thus the presentation of the silk balloon is the reproductive equivalent of the ‘max out your credit card on her’ approach.
The balloon fly species Hilara sartor feeds on nectar, so the actual presentation of prey would be no use to the female. However, as a culmination of this sequence of evolutionary events, the presentation of the carefully woven (but empty) balloon is a species recognition cue.  
The University of Winnipeg's website makes a very good analogy:
The ritual has evolved into bringing something that was once associated with food. It is as if, over evolutionary time, a suitor wooed a lady with diamonds, then with a box containing diamonds and finally with an empty box.
- Kessel, E. L. 1955. The Mating Habits of Balloon Flies. (Diptera: Empididae). Syst. Zool. 4: 97-104.