Mild Water Pepper,  Persicaria hydropiperoides
(formerly called Polygonum hydropiperoides)
Polygonaceae or Buckwheat Family

Sprawling, weak-stemmed plant, 1/2 to 3 feet long.  Pink to purplish, sometimes white or green tiny flowers, in dense spikes at top of plant.  Leaves lance-shaped, strongly veined, not opposite.  Stems jointed, and above each joint they are surrounded by a membrane called a sheath.  Blooms in late summer.

Native of wet places.  In Wildwood found in wet ditches along the bikeway.

Smartweeds (genus Persicaria) all have the tiny flowers in spikes, and jointed stems with sheaths.  Lady's thumb (P. maculosa) is very similar, but likes drier, waste places, is more erect, has long hairs on the sheaths, and has blotches on the leaves..
 

 

closeup of flowers

 

Leaf sheath