I’ve been going out with this guy for a few months. He loves to tease me. When I get upset, he says he’s not serious about it. He makes fun of things I do or say and says these things in a funny way. He never does this in front of others. Is this a sign that he loves me? When I ask him why he acts like this, he says he loves me and this is his way of saying he missed me whenever we've been apart.
His actions are not out of love. He either doesn't know how to communicate his affection in a non-teasing manner, or he is with you so he has someone to tease. Either way, he has a little work to do — and you might need to give him the freedom and space to do that (read: get away from him so he has the chance to learn a new way to communicate).
It’s also possible you’re a little sensitive to lighthearted comments, but even if that is the case, it is still wrong for anyone (especially someone who claims to like/love you) to take advantage of that by teasing you. By all means take note of your own sensitivities and see if you’re not reading more into it than is said. Again, though, this does not mean you deserve to be treated unkindly (even a little bit) and it is not justification for someone to treat you unkindly.
When the teaser sees you’re upset and still teases, he takes it from lighthearted to mean-spirited. In turn, he takes you from treasure to target. That he doesn't tease you in front of others is a big Uh-Oh, and could well be a sign he is grooming you for future, escalated abuse.
Grooming is what abusers do when they wish to train someone to take their abuse, hopefully for the long term. Abusers pick a person with little confidence and few boundaries and lock them into a pattern of putting up with their crap by gradually building on the intensity and frequency of their abusive behavior.