During the past five weeks, I have been losing 1 to 2 lbs per week. I've lost the weight mainly by watching my caloric intake and doing
HIIT three to five times per week.

About 1 1/2 weeks ago, I started incorporating light weight training (essentially circuit training twice a week) as part of my workout routine. My caloric intake is the same as it was when I was just doing HIIT, but now I'm starting to gain weight.

Is that possible? And how is that possible, if my caloric intake (and type of foods I've eaten) has remained pretty much the same?

You could very likely be building muscle and losing fat, therefore keeping your weight the same or increasing it. A lot of people who are just starting experience this depending on their body type as well as those who have been training a while, but have their diet approach spot on.

Is that possible? And how is that possible, if my caloric intake (and type of foods I've eaten) has remained pretty much the same?

Muscle weights more then fat does.

Muscle weights more then fat does.

I need to clarify something. Muscle weights the same as fat. A pound of muscle is equivalent to a pound of fat. Muscle has a smaller volume than fat, so if you had the same volume as each other then muscle would weight more out of the two.:D

Nice clarification.... I didnt know people had to be told a pound of something is equal to another pound of something.... Did you know a pound of white rice is the same as a pound of pure iron... ? it really is

I'm sure that's what he meant, wise-asses :P

Anytime anyone ever said "muscle weighs more than fat" it just never occurred to me to interpret that any other way than "muscle weighs more than fat by volume." I wasn't aware anyone had actually been confused by this.