This argument can actually work both ways and hence requires some clarity in understanding. Remember, a weak rupee is likely to help export-oriented sectors like software, pharma, and textiles. What we are referring about here is the weakness in the rupee due to macroeconomic concerns. For example, in mid-2013 there were concerns because the current account deficit (CAD) had touched a high of 4.5% of GDP (currently the CAD is just 0.1% of GDP). This led to a run on the rupee and the INR fell from 54/$ to 68/$. This also resulted in a large scale sell-off in equities as a weak rupee wipes away the dollar gains of FIIs. When the INR gets wobbly, it is best to sell equities and exit markets.
Look at the current market situation. The rupee is already at 71/$, the Current account deficit (CAD) is getting closer to 3% of GDP. What should you do? There are 2 things to remember here. Although the CAD is going up, the reason is more due to higher oil prices which are pushing the rupee down. Secondly, even when the rupee goes down, there are many companies that earn in dollars, pounds or Euros which will benefit. For example, there are stocks in sectors like IT, Pharma, auto ancillaries etc, which are predominantly export driven. These will stand to benefit immensely from a weakening of the rupee.