I tried various improvements, and found out it looks better if you push the starting point a bit away from the next point, and if you add an intermediary final point.
Test code:

1. void setup()
2. {
3.   size(400, 400);
4.   smooth();
5. //  scale(4);
6.   shape16();
7. }
8.  
9. void shape16(){
10.   float[] points =
11.   {
12.     300.0, 302.0, // Start a little lower and to the right
13.     270.0, 296.0,
14.     272.0, 269.0,
15.     360.0, 213.0,
16.     394.0, 299.0,
17.     350.0, 308.0, // Intermediary lower point
18.   };
19. //  scale(.25);
20.   fill(255,0,0);
21.   noStroke();
22.   beginShape();
23.   for (int i = 0; i < points.length; i += 2)
24.   {
25.     curveVertex(points[i], points[i + 1]);
26.   }
27.   // Loop on the start
28.   curveVertex(points[0], points[1]);
29.   // Twice give a better result!
30.   curveVertex(points[0], points[1]);
31.   endShape();
32.   noFill();
33.   stroke(#008888, 100);
34.   for (int i = 0; i < points.length; i += 2)
35.   {
36.     ellipse(points[i], points[i + 1], 5, 5);
37.   }
38. }

Note: using an array of points allows to quickly and easily visualize the points (the ellipses I added). You can even make only one function and pass it the array and a color as parameters.

I found that using curveVertex() is delicate and can lead to curious results in some cases (like the path reversing and making a sharp corner).
Perhaps because I am used to vector drawing programs like Illustrator, Corel DRAW! or Inkscape, I prefer bezierVertex(), whose control points can be hard to master, but leading to more consistent / logical / expected results.
Moreover, there are tools for the PDE allowing to draw such curve and to convert them directly to code.

You can also check with it: don't duplicate the 1st point, and add the 2nd and 3rd points before ending the shape: