You didn't mention any fuses. I hope that you do have some and you just didn't bother explaining in that detail.
Going all the way back to the battery to pick up power AND ground is definately the right way to do it. Had they attempted to connect the lights and/or amp to the boats original power panel it would have worked very poorly and would have caused all sorts of problems. As long as they put fuses to the amp and lights then you should be okay.
The amp should power up and down based on a signal from the head unit. Most amps have lights of some sort on them so you can see when they are on. If the amps turn on when you turn the stereo on, then turn off when the stereo turns off you should be fine.
If the amps stay on even when the stereo is off then you need to fix that. The amp should have a connection for a small wire, often labled "remote" or similar. This will connect to the head unit, which often lables the output as "power antenna" (intended to raise the antenna on a car equipped with an automatic power antenna).
Did you buy the boat new or used? If the boat is new then I would not expect the battery to be bad, so I would look for something drawing power. New stuff added is the likely culprit but be sure you don't have an automatic bilge pump comming on once a minute that draws power.
If you have a multi-meter, know what you are doing and are really careful you can trace down where a current draw is coming from. I am reluctant to describe it because it is sooooo easy to damage the multi-meter....
Basically you put the meter in "amps" mode, then connect it in series with the battery cable. A two week drain would be somewhere in the 0.1 amp range, so you are looking for a small number. If you see the drain, then start disconnecting things until it drops to at least 0.01 amps (it probably will never go to zero).
The problem is that if you accidentially turn anything on, or the bilge pump kicks in, or you touch the meter leads to the wrong spot, or the electrical system draws a little surge when the battery is first connected then you will probably blow the fuse in the meter. Then it will read zero......
If you just can't find the power drain then you can always disconnect the battery when you are done with the boat. A battery switch makes this easy, but it generally isn't too difficult to remove the cable from the battery.
If the battery is a couple years old then it is possible that it was damaged when it was run dead. It is common for a battery that is near the end of its life to really suffer if it is totally discharged.