Got a picture of your milkweed? I believe many different weeds are called milkweed just because they ooze "milk" when you break a stem. Some are more difficult to get rid of while others bow their heads if you just give them a whif of 2,4-d.
GrazonNext for our central texas milkweeds is best in my opinion. 2 4 D will knock it back but you need something with soil residual put on two years in a row to get a good handle on it.
Not sure if will control milkweed, but for last 2 years, 8 oz remedy plus 1/2 oz cimmaron plus has given me excellent weed control with enough residual to control wooly croton/doveweed later in summer. Has much less drift risk and neither are restricted use, so no license required.