I'm sure there must be a word that fits the bill; "like a lot" and "fond" don't really cut. Any suggestions welcomed.
Fond can be considered as more than like and less than love. (Used as be fond of)
Having a strong liking, inclination, or affection: fond of ballet; fond of my nieces and nephews.
Though, it might depend on the context and it can be synonymous to like also. It is usually not used in a romantic relationship and you can both love and be fond of someone. For example, you can both love your niece and be fond of him because you like to spend time with him.
Other than that, infatuation can be considered as an early stage of a true love (used as infatuated with) but it is not necessarily between like and love. It is called puppy love also.
For example, an urbandictionary entry says:
Infatuation consists of people thinking they are in love but when indeed it is just a deep lust or like for another person.
Also, attraction can be stronger than like and weaker than love. (used as attracted to). Though it is usually a physical attraction and you can be attracted to someone you don't like. (an emotional irony?)
In the end, it might be better to use several words to explain the emotion than using a single word that might not be enough. There are different situations and contexts.
I'm fond of "fond". One, because it's a not an everyday word, it does have a little more strength, a little more intimacy than "like". However, it can be, but is not necessarily, romantic. You can be fond of people you love and you can be fond of your friends.
"I fancy you" is too cordial. Besides, if you're in America, it sounds so foreign that it's almost tongue-in-cheek. "I'm fond of you" is not so stilted. It's a very warm word, suited to many scenarios.