Currency exchange is a complex subject with lots of interlaced layers. You can go deeper and deeper and still not explore ever nuance.
In general terms though, weakening your currency imports inflation. This then causes interest rates to rise, and this can hit the economy by hurting businesses as well as consumers, especially if the savings rate (basically the difference between a country’s savings and debts) is low - ie where mortgage lending is high, and people have high debts, increasing interest rates hurt. If they aren’t raised, the currency sinks lower, import costs increase, pushing up inflation until you end up with the Zimbabwean situation of hyper-inflation of 22,000% per year.
Yes, a weak currency does allow for cheaper export prices - or higher profits from exports where prices in export markets are maintained at high levels. This is happening now with Adobe (Europeans pay nearly double the US price), Microsoft (we pay about 50% more), and to a much smaller extent, Apple (about 15% higher over here). It does depend on the product you pick though.
When the pound weakened in the 1980s Jaguar took the decision to maintain Dollar prices and just make more money from sales in the US, although they could have made the price a lot cheaper because of the lower FX values. It’s also possible they didn’t have the money to invest in extra production (the Brown’s Lane, Coventry factory was renowned for being too small for existing production anyway, never mind increases).
I’m not sure that long term keeping profits high from exchange rate variations is a good policy; reducing prices and selling more volume should give you more customers for the future, many of whom will remain even after prices return to previous levels. Future upgrade costs from new customers can far outweigh short term profit benefits over the long term, but executive pay is geared to getting higher and higher short term profits without long term thinking being so important. It’s a delicate balancing act though.
The Chinese economy is benefiting from artificially low FX rates, but their currency doesn’t float and has a fixed peg to the dollar. That means their economic development can be paid for by the countries they export to. You can see their exchange rate is artificially low because they can even undercut products made in India, a similar country with similar levels of economic development.
It isn’t always a bed of roses though, often a weak currency smells more like the fertiliser roses need. You may remember (or have seen the clip again and again) Harold Wilson in the 1960s trying to explain that “The pound in your pocket is worth what it always was” just after Sterling hit a bad patch and was devalued overnight. Of course, he was totally wrong, it really was worth less because imports became more expensive. He was rightly lambasted in the press for that.
In the US, the Bush administration are wedded to income tax cuts, without reducing spending (look up “Pork Belly Politics”). This only really works if you can grow the economy sufficiently fast enough through exporting more than you import. But the US double deficit isn’t just about how much the government spends or receives in taxes. The second part is the Trade Balance: it’s at record highs because no matter what the state of the US economy American consumers are wedded to buying expensive imports on credit, and buy more from overseas than they export.
So, a low currency can appear nice, but while the total volume of exports may rise, the total value of these exports in monetary terms may not change that much. More volume for export also means factories at home working at higher capacity, and as output capacity gets tighter, wages and other costs rise. Meanwhile, the value of consumer-led imports does increase in cost. This all adds to more inflation.
Basically, both the US government and the US consumer are living beyond their means, funded by a pile of debt that ultimately is owned by the large exporting countries - mainly China and Japan. That’s why politically the US cannot threaten China much, because if they did the Chinese could dump dollars and cause a real crisis in the US as well as the world economy.
One of the many hidden reasons for going into Iraq was because of the threat by Saddam to price Iraqi oil in Euros, not USD, and other oil-leaders were thinking the same. That would have hit the Dollar’s reputation as the world’s reserve currency (it took over from Gold some years back).
So, unless the US consumer stops buying so much imported stuff - such as more attractive cars and luxury goods from Europe and Japan, cheaper electronic goods from China and the Far East and less oil from everywhere - then the Dollar will remain on a downward path. And ironically, giving disproportionate tax cuts to the rich and wealthy actually stimulates more imports of luxury goods, increasing the Trade Deficit rather than reducing it.
As I said, I’m only brushing the surface here. I’ll bet you didn’t really want to know that much about it… 
