Update <img alt="http://www.website.com/images/small-Logo.jpg" /> to <img src="http://www.website.com/images/small-Logo.jpg" />
Within webmail, navigate to Settings > Identities > [Click on an identity] > Signature. Ensure that you enable 'HTML signature' and then click on the HTML editor to insert your HTML, http://prntscr.com/3yccs3 and then click on update.