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Use the option linewidth=0.5 in implicit_plot().

Let us illustrate the difference.

Some setup.

sage: p(x, y) = x * y
sage: xx = yy = (-9, 9)
sage: uu = range(-3, 2)
sage: opt = dict(linewidth=0.5)
sage: col = lambda u: Color(sin(u**3/10), 1.0, 1, space='hsv')

Implicit plots with default line width.

sage: sum(implicit_plot(p - u, xx, yy, color=col(u)) for u in uu)

Level sets for the product of x and y

Implicit plots with line width 0.5.

sage: sum(implicit_plot(p - u, xx, yy, color=col(u), linewidth=0.5) for u in uu)

Level sets for the product of x and y