Currency Values, Developing Economies and Balance of Trade For a developing economy like India, where balance of trade is negative, is it good to have a weak dollar or a strong dollar?

Dollar value increases (Rupee, the local currency, weakens), imports (especially of oil) are done at an extremely high price, that leads to pressure on inflation and people (Central Bank etc.) are concerned. Personally as an exporter, we are a viable business today primarily because of a strong dollar, if the currency remained where it was two years back, our business would have made great losses and probably even shut down. 

My thought process is if the local currency becomes very weak, imports would become expensive; while some imports like oil cannot be avoided, many other goods that are imported today would become viable to be produced locally, this means lesser imports in the long run, and similarly since exports would produce more revenue, more businesses would become viable and hence in the long run exports would increase.  This would eventually result in positive balance of trade and the effect would be a positive spiral. 

Given the short term inflationary shock and long term benefits of employment and thereby prosperity, is it generally better if the Central Bank doesn't interfere in currency devaluation and lets the Market find its own equilibrium.  

The primary question stems from the worry that it is a common conception in India that with a strong dollar the country will be doomed.  

If my argument is weak, can anyone explain why?
Currency values change relatively slowly over time, partly due to differences in the rate of expansion of the money supply over time between different countries, and partly due to changes in the terms of trade.

If we compare the Indian Rupee with the US dollar. M2 for the US dollar roughly doubles every 10 years, the Rupee is going up roughly 5 times in the same period. The Indian M3 measure is equivalent to the US M2 measure (M measures vary considerably between countries in what is being measured.) 

US Dollar M2
Indian Rupee M3

This is why the Rupee is getting progressively weaker, and will continue to do so, especially if balance of payments are also negative. The ratio of rupees:dollars is increasing, and so the value of rupees in dollars is falling, as the market tries to maintain equilibrium. 

When the central banks intervene in the currency markets, they essentially use their position to alter the relative value by buying/selling as appropriate. However, in this case they can only do this if they have foreign currency to sell, and with a negative balance of payments, and a rapidly expanding money supply, they are essentially in the position of standing on the sea shore and telling the tide not to come in.

While all of the above is the monetary side of things, as an exporter you're standing on the trade side of the equation, and what you say is quite correct. All things being equal, over time local producers will step in to provide the imports that are now too expensive, exports will flourish, and the situation should reverse itself as you explain. However, that implicitly assumes that money supply expansion rates are broadly similar, and that clearly isn't the case. Unless and until the Indian central bank gets its banking system under control, and slows down the expansion in the money supply, you can essentially rely on continuing inflation, and a weak currency. 

It continues to be an open question in Macro-Economics as to what the 'right' degree of monetary expansion is. However, there is a very strong correlation between countries with low expansion rates, Germany for example, and economic strength. There are a lot of negative effects within the economy when inflation rates are too high due to monetary expansion, fundamentally because it leads to widespread distortion of the price signal.