'Sympathy' is the feeling itself. 'I have sympathy with him'. 'Sympathies' is the formal expression of sympathy, conveyed via a personal message or in writing. 'I'll send my sympathies' 'Please give him my sympathies'. This plural form is in line with other communications expressing feelings - for example 'condolences', 'congratulations' or 'apologies'.

He sent his sympathies to people affected by the earthquake. He expressed his sympathy for people affected by the earthquake.