US and UN actions condemning North Korean nuclear program development are certainly appropriate. Sanctions are a difficult tool to appropriately manage. Too harsh, and you risk hurting the people more than the country's ability to develop nuclear capabilities. Too soft, and you allow the nuclear development to continue. Sanctions must be appropriately calibrated and targeted (where possible) to maximize the effect on the program itself and limit the effect on the North Korean people.
Yes, it's appropriate for the United States and the United Nations to sanction North Korea, because North Korea is not trustworthy. The people in South Korea constantly live in fear of North Korea and what they might do next. South Korea needs help from the United States and the UN so that North Korea doesn't hurt them.
North Korea has an unstable regime that suppress its people and threatens the security of the whole world. Letting them continue to conduct nuclear tests without at least some sanctions, would be condoning their maverick attempts to become a world power, no matter the costs to the environment or even their own people.
North Korea's nuclear weapons program must be stopped. I feel that sanctions don't go far enough and the U.S. should be preparing for military intervention. The U.N. should also be putting intense pressure on China to back away from supporting the North Korean regime. At the end of the day, sanctions will only serve to hurt the North Korean population who are already undernourished. The U.S. needs to take a much stronger position in this region.