I can confirm that some of what lilaznalien says is true, though I'm not sure how much a role insulin plays into this.
First, keep in mind that the type of sugar contained within these fruits, is known as fructose, which is a simple sugar. Simple sugars are instantly absorbed, converted and ready to be used as energy. A sudden increase in simple sugars does indeed cause an insulin spike (which is a Sugar [not Fat] storage hormone). The purpose of insulin is for your body to regulate the blood sugar concentration.
During this spike, what occurs is that the simple sugars are taken away from the blood stream and stored in the liver/muscle/fat tissue in the form of glycogen (another type of sugar used for quick bursts of energy during activities such as heavy lifting). This also results in your body temporarily halting the use of fat as an energy source.
So what this means is that almost all your sugar levels have been suddenly depleted (since its been all shipped and stored), and your body stopped using fat as an energy source.
But going back to the main topic, whats so bad about the simple sugars getting converted into glycogen? Because glycogen is a limited fuel source, our body only keeps a very small amount of it.
So lets say you had a nice good breakfast, cereal (which is probably simple sugars), with milk (lactose, another simple sugar) and some fruits (fructose, more simple sugars).
Let us say you get this insulin spike as a result, and the sugars are converted into glycogen and stored.
You eat your other meals per day, which may result in more sugar storage, or perhaps a low enough level that the sugars are kept around and being used to some extent as you are doing your work out, your walking around, your other activities. Not to mention the fat in the food you probably consumed is also around.
So what happened at the end of the day? You probably, being the average American (not saying you are necessarily fat, but just because we don't have many food choices that are low in calories anymore), haven't done enough physical activity to compensate for what you consumed, much less those that were stored.
If you didn't consume enough of the simple sugars within your day, the glycogen will not convert back to simple sugar and instead will be converted into an unlimited storage source (unlike glycogen), fat.
In conclusion, if you eat too much fruits, you can gain weight as a result of fat that were deposited because your body had to do something with the sugar concentration that weren't being used.
Therefore, if you are somebody who consumes a lot of fruits, be sure to either limit your fruit intake, or stay active in order to lower your blood sugar level and make use of as much of your extra glycogen as possible, or try to balance out your sugary meals a bit more apart from one another so that you don't get as many insulin spikes.
I hope this information will be of use to you.
P.S.
Fun Fact:
By the way, this insulin spike when eating too much sugary stuff, is why some people experience a sudden weakening in energy or what is known as an energy crash because the insulin removed most of your usable sugar for energy.
Fun Fact 2:
Since insulin is a storage hormone that regulars blood sugar levels, this is why insulin is used medically to treat Type I diabetes (those with a problem to have too much blood sugar concentration).
Fun Fact 3: I'm really sleepy.