How much does it weigh?

Stand on your bathroom scale with it and without it and compute the difference.

The best choice to support a heavy object is to use a sturdy hanger and make sure it goes into a stud behind the wallboard/plaster. If not possible, pay a visit to a hardware store or Home Depot type place. There are many products available to support hanging weight.

The plaster in our house is hard as concrete. For years we did not put any new holes in the wall, but simply re-used the holes previous owners had made. The positioning was good relative to our furniture, fortunately. That meant we had only five things hanging in the whole house. Wait-- our son had some things taped to the wall in his bedroom; tacky but temporary. Since the availability of 3-M Command strips, we have put up a lot more art.

My basic answer is that it might work to reuse the same hole, though you might need to use a larger nail, screw, or whatever than was originally in that hole. If your plaster is as hard as mine, you will need a drill to enlarge the hole even if you do not sink it into a stud.

There are also things that you can purchase at hardware stores that once inside a wall will expand. What they do is spread the stress over a slightly wider area but also allow an old hole to be reused if that hole has not been damaged. If you have a knowledgeable hardware store they can direct you to what is best used in your situation.

I prefer nailing into the studs but some pictures you might need to use several studs to make the picture more secure.

This may not be a good idea, but could you use the same hole, and then add some of those comand strips one to each side to spread the extra weight?

So it turns out my internal scale is way off. The picture weighs 7 lbs and it appears to be on a 20 lb hook but only in the drywall. The other picture was 5 lbs. I don't know why I thought it was considerably heavier. My imagination I guess. However, I did what Graywing suggested and stood on the scale with each picture. The hook is not on a stud but I read on the internet that the angled nail will hold up to 20 lbs in dry wall.

I recently hung a 30 pound mirror without help and used two 30lb. Hooks for the 40 pound wire to hang on. It said to use a hook on each side but since I was doing it alone and hard to see if it was level, I went for two hooks at the top. So far.....its still hanging...and looks straight! :)

Edited to say the angled nails work well. Mine weren't in a stud which is why I used two of them.

Another option is a "French Cleat" also called a Z-Bar. Comes in many sizes.

https://www.homedepot.com/p/OOK-Hangman-13-Piece-French-Cleat-Picture-Hanger-Kit-with-Wall-Dogs-55312/202341625