The Sermon on the Mount is not a new "set of rules" nor is it "another way to read the law" it is a description of the evidence that our hearts are in fact being transformed by the good news that the Kingdom of the Heavens is among us. It is proof that we are good trees bearing good fruit.
In Chapter 6 we get to "religious" activity. Prayer, worship, serving and giving either flow from our desire to justify our lives or to "earn points with God" or to avoid the wrath of a vengefully God OR they are the natural ebb and flow of a life in grace. When we turn these things into laws they simply become another dead end religious activity. When we realize that communing with God in prayer (5-11) is not a "religious" requirement but the way in which our restored relationship with God is fed and nourished we are beginning to live into Kingdom values. When we realize that giving alms is not something we do so that others will see what great people we are or out of guilt and obligation but rather is the natural response to grace that has been lavished into our lives we are beginning to live into Kingdom values. When we engage in spiritual disciplines like fasting not because we believe they earn us credits with the Almighty but rather are seen as disciplines than help us living into Kingdom values we are free of the restrictions of the law and are beginning to live into grace.
When we are concerned about earthly treasures we will never know the freedom of eternal treasure. Because where my treasure is there my heart will be also. NOTICE: Jesus does not say what we usually say. We usually say we value what we love. Jesus says we love what we value (where the treasure is there is my heart). This is an argument against idolatry in all of its forms. Whatever has the highest value in my life owns my heart as well. Think about it: what has the first claim, the first priority, the first energy of my life. Whatever that is owns my heart and is my god. People put all kinds of good things in that central position -- their families, their jobs, their countries, their health, their homes, their education, their reputation, their ministries -- but if we put first value on anything short of God we are headed for a spiritual train wreck and have missed kingdom values -- 6:33 seek first the kingdom of God and his righteousness and all these things will be added to you as well. C.S. Lewis once paraphrased if I aim my life at Heaven I get earth thrown in -- if I aim my life at the things of earth I end up with neither.
Worry is evidence our hearts are not being transformed by the power of God. The opposite of worry is trust. If I believe that God will provide and I have surrendered the need to build my own kingdom, I will be living into the values of the kingdom of the heavens. The truth is I cannot screw up my courage and force myself to trust God. The reality is that trust is borne of relationship. If I am living in right relationship with God (understanding that my forgiveness and restoration and acceptance is a done deal) I will live life in trust. Trust can not be simply given it is earned and built through relationship. Don't worry about tomorrow -- tomorrow has enough trouble all by itself -- Deal with today's stuff, today.