Delta is the ratio of change in the option compared to the change in the underlying. Delta is also an approximation of the probability that the option will expire in the money. It's an approximation because its value is affected by other factors, primarily implied volatility (IV).
In your example, the $44 call has a delta of approximately the 98 to 99 (or more), depending on the IV. That means that the probability that this option will expire in the money is approaching 100% and therefore, there is no risk premium (time value). Because the delta is near 100, the call's price will move close to $1 for every $1 that the underlying moves (as you observed).
Dividends affect option premium as well. The higher the dividend, the greater put prices will be and the lower call prices will be. So if there is a decent sized dividend, you will often see that the bid of deep in-the-money (ITM) calls will be even less than the intrinsic value.
This leads to another concept, namely using high delta deep ITM calls as a substitute for stock ownership, preferably with LEAPs. The drawbacks are not receiving the dividend (if any) and paying a small time premium. The advantage is that there is less risk should the underlying collapse, especially before expiration. Google "Stock Replacement Strategy" and "Poor Man's Covered Call" for more information.