Based on your photos you have variable leaf pondweed. It's a little tough to tell, because the plant picture is short on details I need for a positive ID. If you can, you might want to contact http://www.miseagrant.umich.edu/people/brandon-schroeder/ at Michigan Sea Grant and he might have more local details and be able to assist with plant ID. Be sure of the ID - If you aren't treating the right plant with the right material, you are wasting your time and money.
I'm pretty sure about the pondweed ID, and it is a native plant that is great for fish habitat and pond health. If you feel the need to control the amount (a healthy pond will have 30% native vegetation to support fish and wildlife), you can treat with herbicides. However, that is like cutting grass, and is not a permanent fix. Long-term, we find most plant problems are nutrient problems. A vegetated buffer of 6-10 feet is desirable rather than cutting to the edge of the pond to intercept runoff and nutrients. Resident Canada goose populations will add lots of bacteria and nutrients and should be discouraged. Fertilization of lawn areas around the pond is not a good idea, and should be avoided. for more information on pond ecology and plant management, visit http://extension.psu.edu/natural-resources/water/ponds. The permitting information is not useful for Michigan, for that, speak to Brandon, but the plant management information all applies.
In general, pondweeds can be limited by using a shading agent in the spring (when most management should begin) like Aquashade. Aquathol-K, Komeen, Reward/Weedtreen-D, and Sonar all work on pondweeds, but I don't know which ones are approved in Michigan. Treat no more than 1/3 to 1/2 of a pond at a time if you have heavy vegetation to avoid fish kills from depleted oxygen.