When driving a Class B truck (for a company) are you required to enter scales? And do you have to keep a log book?

Yes you need to enter scales.

Yes you need log book unless your under 120 miles in your home state for the day. Then you still need to keep a time/report sheet that shows where you loaded/unloaded/at what times.

how much weight per axle?

That depends on the axle configuration.

You can have up to 20,000 lbs on the steer axles if it and the tires are rated for that much. Most trucks however are more in the area of 12,000 lbs.

A single rear axle is 20,000 lbs
Tandem axles less than 10 feet apart is 34,000
Tandem rear axles more than 10 feet apart is 20,000 per axle.

Thanks guys

And even that can change depending on what state you run in. Many east coast states allow more weight per axle.

I'm going to mainly be in Virginia, West Virginia & Tennessee

Any CMV over 10,000# is required to stop - I learned that the hard way when I used to race. An 8000# pickup pulling a 6000# trailer for the purpose of making money (even if its a weekend warrior purse) is subject to the laws of a commercial vehicle including taxes, tags, and drivers license.

My friends company just got shut down because his guys were driving 12000# panel vans with no DOT cards or class c permits - BIG fines.

Virginia goes by what Uturn told you.

West Virginia will allow more, Can't remember how much, but you have to make sure your apportioned registration has your max gvw or you will be out of luck.

Tennessee, I dunno. Maybe you will get lucky and the blue bandit will swing by and be able to answer that one

It goes without saying but, You can under no circumstances go over your GVW printed on that sticker on your door.