S. R. Faruqi:

ʿalāqah = relationship, connection

This verse too is of the same kind as

{1681,3}.

The meaning of minnat is 'kindness, benevolence'. But keeping in view Mir's style, its meaning can also be 'pleading, flattery'.

From mat burā māno , the possibility emerges that the addressee-- that is, the beloved-- has some other beloved, not the speaker.

An ʿalāqah is also the name for a cord or noose. In this way it forms a zila with bār , since a burden is tied with a rope or cord when it's picked up.

FWP:

SETS == DOUBLE ACTIVATION; MULTIVALENT WORDS ( minnat )
MOTIFS
NAMES
TERMS

The second line takes full advantage of the spectacularly multivalent minnat , which has opposite and yet complementary meanings (see the definition above). It can mean 'kindness, favor' (that is, what the giver offers to the receiver); and also both 'entreaty, supplication' and 'thanks, praise' (that is, what the receiver offers to the giver both before and after receiving the favor).

In English we can speak not just of a heavy 'burden of indebtedness' (which can have a moral as well as a financial sense), but also of an oppressive 'burden of gratitude' for favors rendered. The parallel metaphor in Urdu is the taking up [uṭhānā] of the burden [bār , bojh] of such obligations.

So what kind of 'burden' has the addressee taken up? It could be the burden of showing kindness and favor and courtesy (to an importunate lover); or the burden of supplication (one is forced to beg and plead for the beloved's favor); or the burden of offering thanks and praise (the humble gratitude that one owes to a generous giver).

The first line makes it clear that the 'burden' might be painful or disagreeable to the addressee, and that it comes from having one's heart 'attached' to someone. The addressee (who can hardly be anyone other than the beloved) either has come to feel a bit of (resigned?) affection for a faithful lover, or has herself become a lover (of the speaker or someone else) in her turn.

Then, the cleverly wide-ranging ʿalāqah (from an Arabic root meaning 'to be attached') is doubly activated: it can refer either to a 'relationship, connection' or, as SRF points out, to a physical 'rope' (see the Steingass definition above). So the second line is made the 'proof' of the first line in a double sense. Metaphorically, when would you ever have taken on such a 'burden' [of minnat] without a tie or connection to the other person? For even physically, when would you ever have picked up such a burden without a rope (with which to secure it)? These are of course rhetorical questions: the answer is 'never'.