Looks like Peperomia obtusifolia which needs more light. When the weather warms up it can go outside for the summer. And I assume it has been thoroughly watered since moving?

I agree it needs more light, what kind of potting soil did you use? When you say you watered it well, did the water run out the bottom of the pot?

Hi again. You're a big help this morning, Flora. :-) Yes, that is definitely Peperomia obtusifolia, I just looked it up. I'm surprised you could ID it from that photo. Not exactly easy to see the leaves. Yes, It's been kept moist since I repotted it. Can I do something about it leaning over? Can I cut the heavy top growth off and if I do, how will it regrow? Can I stick the top growth in water to root?

Christine - Yes, I sat it in the sink and drenched it, water ran out the bottom. I'll do it again today too. I can't remember the potting soil I used, but it should have more perlite in it. I believe it's soil less mix.

I wouldnt water it again since you did drench it, you could use a chop stick to hold it up until it can stand up rite on its own after you get it more light, mine refused to stand up rite, so I just let her do her thing..

I could do that, but would you not recommend cutting it back and using the top growth to start another plant?

It depends on the look your going for, I started out with 1 clipping from a neighbor and within 2 years she filled the pot with new growth, they grow really fast in the summer. Here's mine, I like the solid,

Christine. Oh - so this is like a sprawling plant, not really meant to be upright?Maybe I just had the wrong expectation for the plant. :-). Nice plant and a good amount of growth for 2 years.

To the question about propagation, yes, Pep stems take root easily. Taking a cutting is an option if you're wanting to multiply your plant.