You are 100% wrong.

The old lease doesn't matter. The 30 lb limit is your new lease aka the new contract that you agreed to. Unless your new lease contains a grandfather provision then you are in violation of your lease and can be evicted.

well first, you cannot just ask someone to get rid of their dog in a day.

Technically you are correct. In OH you can be issued a 3 day notice to cure or quit at which time your landlord can go to court to get you evicted.

"well, you are going to have to get the police here if you want my dog gone."

That's exactly what would happen if you act like a complete blockhead and the Sheriff has to come remove you. Then you will have an eviction on your record and will find it very hard to rent anywhere else.

If your landlord will not budge then you either need to get rid of the dog, move (and owe rent until a new tenant is found), or face eviction.

but youre allowed to make changes to the lease? That isnt fair

It's absolutely fair. You agreed to a 30 lb weight limit in the new lease you signed. If you didn't agree to it then why did you sign it?