This is my field
First question is have you got alloy or timber windows?
Next is how much do you want to spend?
How double glazing works is how oeminx has mentioned
The basic DG unit is 4mm glass/ 6mm AIR space/ 5mm glass with the thicker glass to the inside
As Ryan mentioned, you can gas fill the units with Argon. Argon gas has insulation values in itself and the cost is about $20 to $30 per square meter.
All the units should be the same makeup so that that have the same values as far as insulating or if one is more efficent than another, you will still get "crying windows"
Next thing is you should get every window in the house done as the dampness will be in every room. You will need to change your window frames to cope with the thicker units. There is a system called "Retro Fitting" but the frame that the units are glazed into look as ugly as sin and being made from alloy, they create a path for heat to escape and cool to come in around the edges as well as possibly defaluing your home..
After you have mainly solved your window condensation problems, you have to ask yourself where has all that moisture gone that was inside the air in your home? the answer of course is that its still air bourne or has found another place to sellte/gather. This is normally under the furniture or beds.
If you were to be doing renovations I would recomend double glazing withour any hesitation at all but if your heat pump isnt doing the job, its either too small (or you need a 2nd unit) or your not setting it correctly
In winter, we have our aircon unit set on heat through the day and on dehumidify at night, if theres no-one home through the day, set it to dehumidify through the day as well. As you know, it only takes a couple of minutes to heat the home when you arrive back after work.
The thing to remember is that the only reason your getting crying windows is because of the moisture in the air so you should be aiming to reduce the moisture rather than hide the problem