Severance Payments

After a recent layoff, I have started receiving severance payments from my employer. The payments are weekly, the same gross amount as when I was employed. But these payments are being taxed at a higher rate. As far as I understand severance is only taxed differently if paid in a lump sum (due to tax year estimating). When I reach out to payroll, they only respond with “severance pay is taxed higher”. 
I am in Georgia, the severance agreement states that “payments are to be made for 12 weeks equaling last recorded salary gross pay for a total of $****”. 
Is there something I am missing? Or do I get the tax difference back when I file? Just doesn’t sound like they are applying the taxes correctly.