Sikhs were not entirely unified in their desire to join the republic of India. Many Sikhs opposed the partition entirely, and some even preferred Pakistan.

Sikh leaders were actually offered a very generous deal by Jinnah to join Pakistan. In the book "The Punjab: Bloodied, partitioned and cleansed", Ishtiaq Ahmed includes a quote from the Maharaja of Patiala where he details an offer from Jinnah:

“We had a drink and went in to dine. The talks started, and offers were made by Mr Jinnah for practically everything under the sun if I would agree to his plan. There were two aspects. One was based on the idea of a Rajasthan and the other one for separate Sikh state — Punjab minus one or two districts in the south. I had prolonged talks with Master Tara Singh, Giani Kartar Singh and other Sikh leaders, and all the negotiations on behalf of the Sikhs were within my knowledge. Indeed, in some ways I had quite a deal to do with them. I told Mr. Jinnah that I could not accept either of his two proposals, and told him a lot of what was on my mind. Liaquat Ali Khan and Begum Liaquat Ali Khan, and told him a lot of what was on my mind. Liaquat Ali and Begum Liaquat Ali were most charming to me, and went out of their way to offer, on behalf of the Muslim League, everything conceivable. I was to be Head of this new Sikh State, the same as in Patiala. The Sikhs were to have their own army and so on. All these things sounded most attractive, but I could not accept them as being practical, and neither could I in the mood I was in, change my conviction. The talk lasted till past midnight. Lord Mountbatten was a patient listener, occasionally taking part. He eventually said that perhaps Mr Jinnah and I could meet again at some convenient date.”

Another included quote from Hardit Singh:

“Jinnah started by saying that he was very anxious to have the Sikhs agree to Pakistan and he was prepared to give them everything that they wanted, if they could accept Pakistan. I said to him, “Mr Jinnah you are being very generous, but we would like to know exactly what our position will be.” Jinnah retorted, saying “you will have a Government, you will have a Parliament and you will have Defence forces, what part will the Sikhs have in all these.” He further said, “are you familiar with what happened in Egypt? I will deal with the Sikhs as Zaghlul Pasha dealt with the Copts (the Christian minority) when Egypt became independent.” He then went on to tell us the story. According to Jinnah, the Copts when they first met Zaghlul Pasha put forward some demands. After listening to them he advised them to go back, think the whole thing over and come to see him again with a paper incorporating all their demands. They did this. Zaghlul Pasha took the paper from them and without reading it wrote on it “I agree.” Mr Jinnah added, “That is what I will do with the Sikhs.”

Hardit Singh further recalls, “This put us in an awkward position. We were determined not to accept Pakistan under any circumstances and here was the Muslim Leader offering us everything. What to do?”

So as you can see, Sikh leaders did consider joining Pakistan.

Now, as for why Sikh territories would ultimately join India, it's a little less clear and more speculative but I will list some of the contributing factors.

• Religious conflict. In most examples of religious conflict, Muslims tended to treat Sikhs and Hindus as the same in times of conflict. Not only did this create some animosity towards Muslims, it brought up concerns as to if Sikhs would even be safe in Pakistan despite Jinnah's promises. This concern may have proven valid, considering the partition led to many Sikhs in Pakistan being attacked or forcibly exiled.
• Many Sikhs were opposed to the partition entirely.
• Concerns that the Pakistani government would go back on their promises, should something happen to Jinnah. Continued from the above quote:

Then I had an inspiration and I said, “Mr Jinnah, you are being very generous. But supposing, God forbid, you are no longer there when the time comes to implement your promise?”

“His reply was astounding”. He said, “My friend, my word in Pakistan will be like the word of God. No one will go back on it.”

• Many Sikhs had family relations with Hindus, and intermarriage was not uncommon. By choosing to join Pakistan, it can be assumed many Sikhs would have been cut off from some of their family, who would have likely chose to join India.

I hope this can give you an idea of why India would be more desirable to Sikh leadership.