Heavy exercise will typically make you retain water. If you lift heavy regularly, you probably won't notice a weight gain because you're constantly in that "mode". However, if you normally only do light jogs and walks and then all of a sudden you start sprinting, benchpressing and deadlifting, yes, your "weight" may go up.
Weight is pretty meaningless. I suggest you get a fabric tape measure so you can keep track of the inches on your waist, arms and thighs. That'll give you a much more accurate representation of fat loss. Weighing yourself regularly will only drive you crazy. I recommend a weigh-in once every month or so.
Don't put your trust in anyone on this forum, including me. You are the key to your own success.