Craig Thomas has run the Namibia-focused miner since 2015, after being promoted from COO.
Weatherly had to push back a loan repayment due to Orion Mine Finance on March 31, and has seen a precipitous fall in its share price recently.
A three-year peak in mid-February of £0.023 (US$0.032) per share came before more announcements about the financial situation, triggering the 70% fall to £0.0068/share following Thomas' resignation.
In December, Weatherly announced it would buy Intrepid Mines' (AU:IAU) Kitumba project for £2.6 million in cash.
The project has not been a major boon for miners in the past, although Intrepid has asked for an extension to get the deal done so it is not a certainty.
Weatherly said it would scale down the copper project to make it work.
Thomas will leave the company on July 4.