Why does Polonius spy on Laertes?

Polonius is spying on Laertes because he is concerned about Laertes' increasingly reckless behavior and the potential consequences it could have for his family. Laertes' impulsive and passionate nature, combined with the great love the general public has for him, has led him to make rash decisions that could have disastrous consequences. Polonius is aware of the potential danger of Laertes' actions and wants to make sure that he is not making any decisions that could lead to further tragedy for his family, as evidenced by the events that unfold in the play. Polonius is also concerned about Laertes' moral character and is trying to impart his wisdom to Laertes before he leaves for France. He warns Laertes to be true to himself and to be wary of entering into quarrels, as well as to be mindful of his reputation and to be careful with his money. Additionally, Polonius is using the opportunity of Laertes' visit to the court to observe his behavior and interactions with Ophelia, so that he can judge if Laertes' love for her is genuine or if it is a source of his distress.

Here’s the relevant passage from Hamlet:

POLONIUS

My lord, he's going to his mother's closet.

Behind the arras I'll convey myself

To hear the process. I'll warrant she'll tax him

home;

And, as you said (and wisely was it said),

'Tis meet that some more audience than a mother,

Since nature makes them partial, should o'erhear

The speech of vantage. Fare you well, my liege.

I'll call upon you ere you go to bed

And tell you what I know.

KING  Thanks, dear my lord.

[Polonius exits.]

O, my offense is rank, it smells to heaven;

It hath the primal eldest curse upon 't,

A brother's murder. Pray can I not,

Though inclination be as sharp as will.

My stronger guilt defeats my strong intent,

And, like a man to double business bound,

I stand in pause where I shall first begin

And both neglect. What if this cursed hand

Were thicker than itself with brother's blood?

Is there not rain enough in the sweet heavens

To wash it white as snow? Whereto serves mercy

But to confront the visage of offense?

And what's in prayer but this twofold force,

To be forestalled ere we come to fall,

Or pardoned being down? Then I'll look up.

My fault is past. But, O, what form of prayer

Can serve my turn? "Forgive me my foul murder"?

That cannot be, since I am still possessed

Of those effects for which I did the murder:

My crown, mine own ambition, and my queen.

May one be pardoned and retain th' offense?

In the corrupted currents of this world,

Offense's gilded hand may shove by justice,

And oft 'tis seen the wicked prize itself

Buys out the law. But 'tis not so above:

There is no shuffling; there the action lies

In his true nature, and we ourselves compelled,

Even to the teeth and forehead of our faults,

To give in evidence. What then? What rests?

Try what repentance can. What can it not?

Yet what can it, when one cannot repent?

O wretched state! O bosom black as death!

O limed soul, that, struggling to be free,

Art more engaged! Help, angels! Make assay.

Bow, stubborn knees, and heart with strings of steel

Be soft as sinews of the newborn babe.

All may be well.[He kneels.]