Leon is very hesitant when he first meets you, his experiences so far with Umbrella and anything related to it aren't exactly positive, but when you're forced to work together, Leon at least tries to be polite.
Once he learns more and more about you, and your view on the company, Leon finds himself liking you, he no longer sees you as a threat or enemy, and becomes more friendlier and wants to spend time with you.
After a while you both become quite close, he still doesn't trust you completely, not until you do something that really shows that you're on the same side, but he can't deny the feelings he has for you, no longer is he just wanting to spend time with you, he wants to protect and help you.
When you finally reach a breakthrough in the lab (or wherever your specialities lie) Umbrella decides it favours your mind over you as a human, and others want to steal your work and eliminate its creator. Leon and you both escape the facility barely, and after saving his life and throwing your relationship with Umbrella away completely, Leon finally trusts you to admit the feelings he has for you.
Since you're both on the same side now, a relationship is on the table, though not wise due to the circumstances and Leon's job, it's up to you whether you both take the plunge and risk it all for love, or if your work is more important than a certain handsome agent who wears his heart on his sleeve for you...