When we begin to deepen our ability to appreciate things and people, we begin to recognize the value of things and people. This is both a good thing as well as a potential hindrance. It is a good thing because we realize the value of things and people in our lives and are therefore grateful for them, feeling deep meaning from them, and therefore more fulfillment. The potentially negative side of this is that the extent to which we find things and people more valuable, we also may become more attached to them, thinking of their importance to our ego as being heavier and therefore our emotional attachment becomes greater.
First of all, the attachment itself is a kind of suffering since we are always in a place of ignorance with relationship to reality. We always care about the things more form a selfish or self-reflective, insular, neurotic way as opposed to a genuine open sharing and connection. We thing this thing or person is good only for saving me from my pain and we don't value them for their own sake. Secondly, all things and people are impermanent, therefore all things and people inevitably go away or break or die, which will leave us with nothing but exaggerated suffering to the extent of our attachment to those things. Finally, through attachment we overvalue things, making them out to be so much more important than they truly are, when they are no more or less important than our heart and a clear head recognizes it to be.
Appreciation and non-attachment go hand in hand, since if you are truly appreciating something for what it is in the world and not just for what it gives you, then you are free of attachment to any bias or exaggeration. There is ultimately no limit to how much you can appreciate something since all things are sustained by the same fundamental Truth that is the Transcendent. That is the vastness of the ordinary. However, a chair is also just a chair, and a tree is also just a tree. It is both a Divine wave in the ocean of the Universe, and an ordinary thing of life. Respecting both dimensions of things is a magical dance of appreciation that enriches your experience of everything and everyone around you.
In meditation we come to recognize the deep meaning of the moment, one that is beautiful and meaningful, but also one that is fleeting and a radiance, ever-new. Therefore it is not something we hold on to, but rather we allow it to reveal itself. Both appreciation of the moment and complete non-attachment allow for fullness and freedom respectively to be realized. May you come to understand the union of appreciation and non-attachment that your heart may be full and free.