Colour change when excess ammonia added to [Cu(H2O)6]2+
Like the OP mentioned, the replacememt of a weak field ligand ($\ce{H2O}$) by a stronger one ($\ce{NH3}$) certainly increases the $\Delta_o$ of the $\ce{Cu(II)}$ complex. 

A chemical sample appears colored when it absorbs a certain wavelength of light. What we see is the sum total of the remaining colors. The colour visible to the human eye would be the complement of the colour(i.e. wavelength) absorbed. 



The increase in $\Delta_o$ leads to the absorption of a lower wavelength (or higher frequency) of light, as evident from:
$$E=h\nu= \frac {hc}\lambda $$



Note that a higher frequency would mean a shift towards the blue end.

Quantitatively speaking, the light blue colour of the initial hexaaqua complex was due to the absorption of the orange spectrum range of light.

Back to the color wheel, a shift towards the blue side (in the green direction, please) gives us a lighter shade of orange.


  Why does the solution turn deep blue?


Observe the complement(the colour diametrically opposite) of orange-yellow is definitely a deeper shade of blue.