This is from Mathematica v9.What version are you using? Perhaps a bug? :)

    Inv = WeierstrassInvariants[{1, I/3}];
    Plot[Re[N[WeierstrassP[2*x + 1 + I/3, Inv], 100]], {x, 0, 1/2}, WorkingPrecision -> 100]

![Mathematica graphics](https://i.sstatic.net/G6tja.png)