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If your grandson was born a month early there may be a delay in making eye contact (usually happens between 6-8 weeks). He may be three months old but developmentally he is two months old. So for him this may be normal. I'd wait and see what happens in the next couple of weeks. Please accept so I get credit for my response.
He seems to be developing at an otherwise normal pace, reaching other developmental milestones at appropriate times. He is a very fussy baby, though.
If he weight 7 lbs 8 oz he may hit most developmental milestones. If he went full term he may have been a much bigger baby. I would not worry about this for a few weeks and when he goes for checkup mention it to the doctor. If he is a fussy baby make sure he gets swaddled. I find that a great soother. Hopefully he will outgrow the fussiness too.