Alas, your photo shows a bad weed. Here is what my book says of it on page 248:
Corn Bindweed (Convolvulus arvensis). The name
Convolvulus is derived from the Latin
convolvere, meaning “to entwine,” and
arvensis, meaning “of the fields.” It thrives in sunny, cultivated ground. This common weedy European
perennial grows from rambling, starchy
roots; the tops die in winter. It blooms mostly from May into July; flowers are ?–2 inches wide and shallowly funnel-like. Colors are white, pink, or mixed—set off prettily against deep blue-green foliage of arrowhead leaves. No soil is too dry or site too sunny and hot. It would make a swell drought-tolerant garden ornamental if it didn’t insist on conquering. Each stem trails along the ground or wraps itself around something, and the whole plant merrily twines along. Some call it: small, field, or lesser bindweed, devil’s guts, creeping Jenny, bearbind, ropebind, cornbind, possession vine, and smallflower morning-glory.
Good luck; you better start plucking and plucking.
Arthur Lee Jacobson