(Bruce Cockburn, "You Get Bigger As You Go," from Humans)
While we may forget a great deal as we grow older, it's also true that, as more life has been lived, there are more memories piled up. For one who has had a tragic life, perhaps this is a burden, like "boats in tow" that you can't cut loose. But even with a relatively good life, there is a weightiness to memory.
Solomon was likely on to this. In Ecclesiastes he surveys a life "under the sun" and calls it "[u]tterly meaningless. Everything is meaningless" (Ecc.1:2). Remembering all he had done and all he had tried (he lived what we would call a very "full" life), he basically concluded by saying "what's the use?" He laments the monotony of life, the boredom, the fact that there is nothing really new, and the brevity of life, and says "so what?"
I guess that's the burden of memory if what we see and experience is all there is. For the materialist, if he is candid with himself, there is no meaning. He may say life is what you make it, but that's not even true, as you can't make meaning. All he has is the experience of the moment. And memory? Best to do all one can to forget or reinterpret the past to make it more palatable or happy, as this is all we have. There really is no meaning. That's really the plight of the post-modern, if he is honest. No truth, no meaning, no memory that matters. Pick a narrative. Define your life as you like. Be happy. It's all you have.
On the other hand, the Christian says everything matters, and that everything includes memory. We carry memories for the sanctifying effect they have in our present lives. If we remember a hardship or trial, we also use it as a reminder of God's faithfulness. For example, I'd have to say the two hospitalizations and emergency operations I endured are particularly unpleasant memories, but they are reminders of God's faithfulness and my own faithlessness. They have present sanctifying effect if my memory of them stimulates me to greater faithfulness and reliance upon God.
Memories may be weighty, but they need not be heavy. Jesus says "my burden is light, my yoke easy" (Mt. 11:30). He is the one pulling those bales of memory with us, or even for us. He's the one who bears the weight of our mistakes, our sin, and all the sin of the world. He can carry it. He can handle it. I just need to let Him.