This is not an easy question to answer. To provide context for those who don't know, Pergamon was a small but influential Hellenistic kingdom near the coast of Asia Minor in what is now modern Turkey. In 133 B.C., King Attalus III died and his will revealed that he gave his kingdom to the Romans, who began squabbling over it amongst themselves as the tribune Tiberius Gracchus attempted to use the bequest to fund his land commission. A pretender arose in 129 B.C. and a small revolt ensued against the Roman takeover; but it was crushed quickly and the former Pergamene territory became the Roman province of Asia, though parts of its territory were given to nearby client kingdoms. But why? It's hard to measure the intentions of a figure like Attalus III, when nearly all we know about him comes from much later and Roman-centric sources who only mention the will in the context of Tiberius Gracchus' tribunate.

It's first of all important to note that this wasn't the first will of a Hellenistic king bequeathing a kingdom to Rome. The first we know of was made by Ptolemy VIII Euergetes II (also known as Ptolemy the Obese); an inscription survives from the mid 150s B.C. recording his will to bequeath his kingdom to the Romans if anything treacherous should happen to him. He probably did this for diplomatic reasons; Ptolemy was always in constant conflict with his brother and pretty much everyone else in his family (he loved to scheme) and he consistently tried to draw the Romans in to settle disputes in his favour. This will, published at Rome, might have been one more way for him to try to get the Romans to favour him rather than anyone else in his family: "Look how loyal, I am, Romans!" He may not have actually intended to give his kingdom to the Romans, but he still set a precedent that this was one way to gain Roman approval. The Romans were happy with this, since it gave them some leverage in being able to balance powers in the Greek east against each other, though they didn't always accept bequests: After Ptolemy XI's later death, the Romans ignored his will which granted Egypt to the Romans and bestowed it on Ptolemy XII instead.

Attalus III had no sons or heirs. So it may have been expected that he would create a will bequeathing his kingdom to Rome. This may have been especially necessary because Rome had, since the 160s, at times undermined the kingdom of Pergamon and been suspicious of it. As Polybius tells us in books 30-31, for example, in the 160s the senate had snubbed Attalus' father Eumenes II when he came to Rome for an embassy, and later may have even sent agents to sabotage Eumenes' war with the Galatians (though some scholars, like Erich Gruen, reject this). So it may have been necessary for Attalus to prove his loyalty with a will. I can't say what his expectations were. Maybe he thought that the Romans would reject it and maintain the kingdom. Maybe he thought that he would eventually have a son and could change the will then. He did die in his thirties, relatively young. Or maybe it was clear that the Romans wouldn't tolerate Pergamene power anymore and he fully expected they would annex his kingdom no matter what, since he had no heir. And Sallust has a "letter" of Mithridates in his fragmentary Histories which claims that the Romans fabricated the will to annex the kingdom. What answer you choose will probably depend on how imperialistic and aggressive you think the Romans were at this time. Unfortunately, I think we can only list possibilities for why he did it.

Further reading: Erich Gruen, The Hellenistic World and the Coming of Rome.