Weight belt rule of thumb - the weight should make you neutral at about half the depth that you expect to be diving.
Yes. get a belt and some weights. Well worth it. Do make sure though that you are correctly weighted.
Keep in mind that you would idealy like to weight yourself in order for your airways to be clear of or at the least level with the water surface when you exhale all your air.
This aparently is a safety feature which help in the event of a blackout. What happens when one becomes unconcious is that your muscles relax and the air is forced out of your lungs and if you are weighted too heavily you will sink even if you blackout with your head above the water.
Diving with lungs jam packed full of air would make you very boyant and not help you for relaxed dives.
getting comfortable diving with passive exhale, or less than a full breath of air would help your duckdive down easily, yet correct weighting shoudl still return you to the surface when you stop kicking, but not like a cork.