S. R. Faruqi:

The saying is, 'he would kill a heron, in his hand would be a feather' [baglaa maare par haath] . That is, although the heron is seemingly a very large and substantial bird, in reality it has very little meat; it's basically nothing but feathers. This saying is used when people want to say of someone that although outwardly he is weighty and pompous, inside he's nothing.

Mir has very finely used the saying in the form of a verse and metaphor. That is, because of the Shaikh's hypocrisy/affectation [riyaa-kaarii], the jest of baglaa maare par haath proves true.

Then, the heron is white; thus in the first line he's mentioned the Shaikh's white beard, and established the outward affinity as well between the heron and the Shaikh.

FWP:

SETS == IDIOMS
MOTIFS
NAMES == SHAIKH
TERMS == IDIOM

It's a pity that the Shaikh is such an unattractive denizen of the ghazal world, because the idea that a prey when hunted down is reduced to nothing but 'feathers' is just the kind of mystical-sounding image that sounds right for the lover (who after death is frequently reduced to a handful of flying dust). But of course it's very clear that there's no such romantic intention in this verse; Mir makes very often refers to the Shaikh, and almost always in terms as negative and disrespectful as those he uses here.

In fact there's a widely known proverbial saying, baglaa bhagat , that is used to accuse someone of hypocrisy. It's hard to believe that Mir wouldn't have known it, and wouldn't have felt it hovering above this verse. It's so well established that it appears in Platts (see the definition above); it's even been used as the title of a Bollywood film. One modern scholar, Prof. Khusrau Gurganvi of BHU, explains it as follows:

The Bagula (Ardeola grayii) is a bird that stands in shallow waters on one leg for long periods of time and strikes at the fish once they become unaware of its presence. Bhagat means bhakt or devotee. Standing on one leg for long periods of time made the bagula seem like it was a pious devotee meditating on whatever it was a bhagat of, when is reality it was just a cunning trick to get fish.