I will also agree with the posters saying that going up&down too much may be a symptom of overweighting. The idea is that it is normal to go up when you inhale (increase your volume) and down when exhaling (decreasing your volume), because of the Archimedes law.
Also, because of Boyle's law (P*V=constant), when you go up, all the gases that you are carrying are expanding. And when you go down, they compress. Now, let's assume you have 1 liter of air in your BC, at a depth of 10 meters (2 bar). If you go up half a meter, pressure decreases from 2 bar to 1.95 bar. So we have 1*2=x*1.95, x=1.025 liters (0.025 liters increase in volume). If you have 4 liters of air in your BC, then it expands to 4.1025 liters (0.1 liters increase). So the more air you have in your BC, the more it will expand when your lung expansion sends you up, which will accelerate your ascent even more. The same happens when you go down. This is a chain reaction, so if you breathe too slow it may send you up and down a lot (the more you go up, the more it expands, and the more you go down, the more it compresses). The good news is that it would be hard for the expanding parts of the equipment (exposure suit and BC) to expand enough so you could not reverse the direction by exhaling (a 3-5 liters expansion would be enormous and not expected during a 0.5-1m ascent/descent), so you don't need to be worried about this bobbing - you will be always able to reverse it by inhaling/exhaling (as needed).
In the first part of your dive, depending on your tank, you are 2-3kg heavier than at the end of the dive, so you need to have more air in your BC to compensate. It makes sense to notice a decrease in bobbing in the second part of the dive, for the reasons explained above, because you are carrying less air in the second part. If you are properly weighted, your BC is almost empty, so the air required to float the tank is a significant percent of the total air in your BC.
Please note that there are other expanding parts of your equipment - the exposure suit (wet or dry). About it you cannot do much, because it depends on water temperature. But you should expect more bobbing when diving with a thick suit than when diving tropical in a 1-2mm shorty.
Also, remember that bobbing will be wider at shallow depths, and will decrease in deep water. In our example, 2/1.95 is much more than 4/3.95 (so the same bobbing will be less accelerated by BC/suit at 30 meters than it is at 10 meters).
As a conclusion - exaggerate bobbing (compared to what you know it is normal) means overweighted. But bobbing is to be expected no matter how good your weighting is. Do a proper check if you can, because proper weighting will reduce bobbing for sure - probably enough to enjoy the improvement.