I'm good if I'm moving, but to stop, my lower half tilts down and that's not my goal.
My question is would this be an option in my case? Adding a small weight higher as well?
The lower half tilting down is common in divers that have not dialed in their trim. And you will really be a happier diver once you can get past it, by dialing in trim.
Don't *add* weight higher, *move* some of your weight higher. As a diver, when still, you are just a seesaw in the water. If you're too heavy on one end, you need to move some weight closer to the other end. The general progression of places to shift weight between might be weight belt -> integrated -> lower cam band -> the steel plate of a BP/W -> upper cam band -> top of BC/plate or shoulder strap. It means having pockets to put the weight and weights small enough to move, several 1 lb. weights instead of all in a single 4 lb. weight. Dive gear express has nice $10 weight pockets that work well on cam bands or shoulder straps. They are small, but you do not need much, nor want much in any one pocket. There are also options for attacking hard weights to shoulder straps with bungee cords, that may be suited if your BC shoulder straps do not facilitate adding small pockets. But top cam band is the easy place to start for moving weight higher, just keep it balanced right/left and try to keep it tight to your back.
A bit more refined than just balancing the seasaw is to have at least some on your body, with a weight belt. It makes your rig easier to manage on land and to helps keep you closer to neutral without the rig on. Having this weight belt means the weight on your rig needs to be a bit higher than if all your weight was on the rig, but the top cam band, a steel plate of the BP/W, or shoulder strap weights handle that fine.
The OP's question evolved into how to do that and keep a significant amount of the weight on the body and still be in trim. That is a bit more complicated, as the whole BC/plate takes up much of the upper body real estate. Most scuba divers do not need to venture into ditchable neck weight territory. I would not recommend worrying about neck or wetsuit chest weights, unless you are already dialed in with good trim using the options above. Neck or wetsuit chest weights are not something for a new diver.
Edit: A consequence of weights on cam bands is that they are behind and relatively far from your body. This can make you back heavy and create a tendency to turtle. It all depends on how much you put there, if your tank is buoyant or negative already, and your other weights. The steel plate of a BP/W has an advantage here as it is tight against your back, so not much back heavy effect. Small weight pockets on the back curve of your shoulder straps are fairly tight to your body so should not cause much back heavy effect. As they are far up your body, just a small amount of weight there has a big effect on your head to toe trim. It's all just playground level physics, seesaw, and what kinds of physical options you have in terms of where to put weights.