Depending upon the individual and the type of knowledge, knowledge can be a burden. "Knowledge" is, obviously, a hopelessly broad term, and it would difficult to argue that having enormous knowledge of the world or of medicine or art is a burden. "Knowledge" of someone's declining health, or of one's serious medical situation, however, can be burdensome, although both may require attention. Every responsible adult should be knowledgeable about his or her health, but knowing that one's days are declining by virtue of an incurable illness may cause the individuals in question to withdraw from society and to spend one's remaining time in a deep depressive state. Should certain people not be informed of the condition of their health, or should they be kept ignorant of information regarding another person's health, the knowledge of which would cause undue emotional stress? Under certain circumstances, quite possibly. An elderly family member might be kept ignorant of the condition of another relative if others believe that knowledge would be detrimental to the mental well-being of the elderly individual. Knowledge that a loved one is in serious difficulty is enormously stressful, and children and the elderly are routinely kept 'in the dark' concerning such matters.
Beyond the intimate details of the individual, knowledge can be burdensome if awareness of a particular situation compels an individual to act when he or she would rather not. A president or prime minister who becomes aware that a foreign government has cheated on the terms of an agreement might prefer to have not been presented with that information, as the knowledge of the illegal act in question requires a response that could be deleterious to the broader relationship between the two nations. During the Cold War, some American officials reacted with disdain to the notion that the Soviet Union was systematically violating the terms of arms control agreements. The reason for their discomfort with that knowledge was that it was now incumbent upon these officials to respond, and that response could derail a relationship into which they had invested much time and energy. If they had remained ignorant of the treaty violation, or felt they could comfortably ignore the information, then there would be pressure to react.
There are instances in which knowledge is a burden. It's difficult to argue that people should remain ignorant of certain matters lest they feel additional stress, but, under certain circumstances, ignorance is, as they say, bliss.