benefits to financial leverage - share repurchase

What are the actual benefits towards increasing financial leverage for a company? I understand the favorable tax treatment on debt, but how does the company gain additional tax benefit on debt simply by buying back share and sending out cash?

It lowers its WACC.

But isn’t the WACC based upon market value of debt and equity? And with a share repurchase we are decreasing the amount of stock that is outstanding but not decreasing the total market value of equity

What makes you think that the total market value of equity isn’t decreasing?

Would the total market value of equity be decreasing because the investors are selling their shares back to the company?