Keep the area weeded until the plants are established, after which they will shade out competition. Plant as soon as the danger of frost is past, so the plants will be as large as possible when shortening days tell them to send their energy into the tubers. Cutting the flowers is fine, but don't harvest tubers until frost kills the plants. Shoots continue to sprout but they are extremely skinny, rather than the typical broad, fat shoots. Assuming that's what you have, the problem is most likely the dim location.
Spindly growth is generally a sign of light deprivation.
Dieffenbachias are classed as low- light plants because they don't need or want strong sunshine, but that doesn't mean they will grow in the dark. Try moving the plant to a spot where it will get bright but indirect light, like a north windowsill. Conversation is optional, as long as you don't eat it. The deer have decimated my yews and rhododendrons this winter. Nary a leaf is left.