So when I go through the weight scales and they randomly run my CDL class A, would they see my current parole status? My PO told me he will not let me to officially go out of state for work, but he said that if I just drive and won't get into trouble he will probably never know either. Please help.

That sounded like an okay... when I was on parole I had a similar problem I guess its just a lot of paperwork he rather not do and as long as your name isn't in a police report he will never know

The only officials who can answer your question are the troopers who run the weigh stations and/or the DOT/MVA/DMV employees who know the particular laws and regulations of the states you would be traveling in.
You can take your chances if you choose to, and I think that you are taking on some serious risks. You could have an accident, be overweight, be found to have serious safety defects on your rig if inspected as many states do, at the scales and any number of hazards could result in further investigation (over and above a simple CDL check) - and all this is over and above whether or not they will find it on a routine CDL check.
Members here cannot help you break the law and there seems to be no doubt that it is a violation.

The weigh stations do not run a criminal history on you. (although they can) unless, if your hours are wrong, if you are over weight or for any reason was to get a traffic ticket, yes they run it.

And your PO did not give you an OK, he will deny every saying it, he said, he could not give you an OK, why not ?
he said , it is not ok, and if he found out, then he would have to revoke you.

so what if someone else, hit your truck, you have an accident.
what if your tire looses rubber and it hits another car,

what if they do some random checks

a lot of risk or being revoked.

I would not just ask, but apply in writing for permission, to work and travel
Make them deny it in writing,