Question
I JUST READ ABOOUT USING SUGAR TO KILL DOLLAR WEED.  I KEEP WATCHING FOR IT AND DIG VERY CAREFULLY TO REMOVE EVERY TRACE OF IT FROM THE NEW ST. AUGUSTINE SOD I HAVE IN MY YARD. MY PROBLEM IS NOT DOLLAR WEED. I AM HAVING AN EVER INCREASING PROBLEM WITH A PLANT I PURCHASED IN TENNESSEE.  IT IS A CLOSE TO THE GROUND, FUZZY SAW BLADE EDGED LEAF, MORE INVASIVE THAN DOLLAR WEED NIGHTMARE.  IT WAS NOT INVASIVE IN TN. A PIECE OF IT WAS IN THE ROOTBALL OF A PLANT I BROUGHT WITH ME WHEN I MOVED TO THE FL PANHANDLE. IT GROWS ALMOST EXACTLY LIKE DOLLAR WEED WITH THE FRAGILE UNDERGROUND WHITE ROOTS.  IN THE PROCESS OF ERADICATING IT, I'VE FOUND ITS ROOTS AS DEEP AS 15 INCHES.  IT ONLY TAKES A VERY SHORT PIECE OF THE WHITE ROOT TO START GROWTH.  IT IS IN A 12 INCH HIGH QUITE LARGE RAISED BED THAT IS OUTSIDE THE DRIP LINES OF A 25 YEAR OLD SYCAMORE AND SAME AGE MAPLE TREE.  I'VE SPENT NO TELLING HOW MANY HOURS GENTLY DIGGING IT OUT.  I'VE SIFTED THE SAND (SAND THAT I THOUGHT WAS GOING TO BE DIRT LIKE THE DIRT I HAD IN TN) TO FIND ROOT FRAGMENTS.  I HAVE REMOVED ABOUT 25% OF THIS STUFF.  I HAVE A LOT OF PLANTS IN THIS LARGE BED SUCH AS 8 SMALL JAPANESE MAPLES, SOME PIEERE JAPONICA, SWEET OLIVE, AZALIAS IN ADDITION TO MANY PERIENNIALS.  LARGE HOLES WERE DUG FOR ALL OF MY UNDERSTORY MAPLES, SHRUBS, ETC., IN THIS AWEFUL SAND THAT I FILLED WITH COMPOST I MADE FROM DECOMPOSING CRUSHED LEAVES AND GRASS CLIPPINGS.  I HOPE AT SOME POINT TO HAVE ALL OF THE SAND AMMENDED WITH MY COMPOST.  IN THE MEANTIME, I WOULD LIKE TO KNOW IF USING SUGAR WOULD HURT MY PRECIOUS LITTLE MAPLES AND THE OTHER PLANTS.  I AM WAITING UNTIL WE HAVE A COLD SNAP OR TWO TO GET IN CLOSE TO MY LITTLE TREES, ETC. WITH MY DIGGING.  I HAD TO NEARLY BAREROOT SOME ENCORE AZALIAS GETTING THE TENACIOUS WHITE ROOTS OUT.  I MAY HAVE TO DO USE THAT METHOD TO REMOVE IT FROM UNDER ALL MY PLANTINGS.  I WOULD BE VERY GRATEFUL FOR ANY RECOMMENDATIONS AND ADVISE.  I HAVE PHOTOS OF THIS AWEFUL PLANT TO SEND IF AN EMAIL ADDRESS COULD BE PROVIDED.  I FORGOT TO MENTION THAT IT GROWS ALMOST EXACTLY LIKE DOLLAR WEED, PUTTING UP ONE TINY LEAF AND THEN 6-8 MORE ON 2" STEMS THAT FORM A LOOSE ROSSETE SHAPE.  UNDERNEATH THIS ROSSETE ARE LOTS OF ROOTS GOING IN ALL DIRECTIONS.  IT LOVES TO GET ENTANGLED IN OTHER ROOTS.   SANDY

Answer
I have no experience with using sugar as a plant killer; although any product applied at a high enough dose will kill - plant or animal!
The  first step is to identify the plant accurately. Try to get a whole plant - leaves, roots and flowers if possible and take it to the County Extension Office (there is one near you).
They will set you on the right track to control the weed.
Click on this link.
Office Locations