Txt messages are very difficult to authenticate in court, so while I won't say the messages are usless, I will say that the court could decide that they're not sufficently trustworthy to admit into evidence.
An arrest, without a conviction also has little weight in court.
Proof of payment is great. Photos with the child is also great -- shows a caring parental relationship is already established.
Marijuna photo while pregnant -- that would impress me if I were the judge reviewing a custody request. Shows that the parent doesn't care about the child, and may have a substance abuse problem.
Pretty good stuff, in my opinion.
Re who gets custody, legally, mother already
has custody. Your son is entitled to joint custody
or visitation, and it is extremely unlikely that the mother would lose custody. The question will be who should be the day-to-day caregiver. That's up to the court, and the judge will want to review all of the facts. The most interesting evidence -- to me -- is the marijuana smoking while pregnant. That shows a pretty careless attitude towards her child.
Your son will have to put it all in front of the judge and see what happens. I don't think any single fact would cause the court to make a decision. Your son would need evidence of ongoing criminal activity, recent child abuse
by the mother, or serious mental or physical disability, which would make it difficult or impossible to care for the child in a consistent manner.
Hope this helps.