The relationship between God and His people is an eternal covenant defined by constant care. Unlike lifeless statues that demand labor from their worshippers, the Creator actively carries and supports His creations throughout every stage of their existence.
The imagery of advancing years and graying hair represents a continuous process of maturation, with graying marking the most advanced stage of life [רד״ק, מצודת ציון, מלבי״ם]. Commentators offer different perspectives on what this aging signifies for the nation. It can be understood as a metaphor for the long timeline of the people, stretching from their birth into eternity, carrying a promise that God will never abandon them [אבן עזרא, שד״ל, מצודת דוד, ביאור שטיינזלץ]. Alternatively, old age represents a period of spiritual weakness. In this view, even when the strength and merits of the people run out, God continues to save them purely out of His deep mercy [רש״י]. Through it all, His enduring presence remains a constant reality for His people [רד״ק].
The primary approach among commentators is to contrast God with the idols of Babylon. Human beings create idols and are therefore forced to bear the heavy burden of carrying them on their own shoulders [מצודת ציון]. When trouble strikes, these lifeless objects are completely unable to save the very people who carry them. God, however, is the Maker of Israel. Because He made them, He is the one who will carry them, bear their heavy burdens, and rescue them from their enemies and the Babylonian exile [רש״י, אבן עזרא, מצודת דוד, רד״ק]. This dynamic is also completely different from human families. Parents carry their children only when they are young. As parents age, the roles reverse, and the children must carry them. God, by contrast, continues to carry His people even as they reach old age, and they are never required to carry Him [מלבי״ם].
On a deeper level, God's role as the Maker of the people is understood as a reference to His creation of the human urge to do wrong. Because God created this evil inclination, He takes a measure of responsibility for human failings. As a result, He forgives the sins of the people and saves them out of mercy, viewing them as somewhat overpowered by their nature. Furthermore, God rescues His people even when they sin to ensure that the surrounding nations cannot claim that the punishments God brought upon them for harming Israel were unjust or without cause [חומת אנך].