There are two ways to solve your
problem:(a) buy the special piece of apparatus designed for the measurement
of the Young modulus
You will find the suggested experiment in the 16-19
Experiment guides.
(b) use thinner wire to increase the extension for a given load. I
suggest you try SWG 32,
Clamp the wire to a suitable point and then hang weights on it
carefully. Using a vertically mounted ruler (graduated in mm) held in a clamp stand close to
the load you should be able to detect the right extension.
If you have a travelling
microscope you could focus it on the bottom edge of the load and measure the extension in
this way.