Dr. Seward is the member of the Crew of Light (the group that fights Dracula) that we know the most about, simply because a lot of the novel is told from his point of view, from his journal entries. And his journal entries aren't all business – he doesn't stick strictly to his medical cases, but rather includes a lot of personal details about how broken hearted he is over Lucy. Sure, he's not the man Lucy chooses – she chooses Seward's friend, Arthur Holmwood. But we never get to read Arthur's journal, so we don't really get to see things from Arthur's point of view. As a result, it's Jack Seward's broken hearted disappointment that really elicits our sympathy, not Arthur's.
We also know that Dr. Seward is a loyal friend: he doesn't get angry or jealous when his beloved Lucy chooses his best friend, Arthur, over him – instead, he invites Arthur out for a drink (5.19). We also learn from Van Helsing that Seward once saved Van Helsing from blood poisoning by acting quickly enough to stop the spread of the poison (9.26). So Dr. Seward is far from being a dry, boring doctor – he's intelligent and clear-headed, but at heart he's a romantic and a faithful friend.