How old are you? I estimated your age to be 30 in this BMR calculator ...
http://www.myfitnesspal.com/tools/bmr-calculator
And it spit out that your resting BMR is 1832 calories a day. If you are not doing a lot of exercise on top of that. Lets assume you are burning about 1900 calories day. The strict IP P1 regimine is giving you about 950 calories a day. So you are in deficit (between what you are ingesting vs. what you are burning of 882 calories a day.
To burn 1 pound of fat, you need a deficit of 3500 calories. Also when you burn 1 pound of fat, your body will release 1/2 pound of "body stored water". So when your total calorie deficit gets to 3500, you should lose 1.5 pounds on your scale.
If you are on STRICT Phase 1 ... your deficit is 882 calories a day, so it should take you nearly 4 full days to burn 3500 calories and lose 1.5 pounds on your scale.
So if you are not cheating at all, and getting 950 calories a day on IP P1, I estimate your weekly losses should be right around 2.6 pounds. (Or about 11-12 pounds a month.)
Now if you start eating more food, such as extra hard boiled eggs or extra IP packs, it should cause you to lose less weight (since you are now getting more calories and have a smaller deficit per day).
What the high protein levels do is keep your body from burning muscle instead of fat. So if you don't get enough protein (by skipping IP packs or not eating 8 oz of lean meat) you will probably lose weight off the scale FASTER ... however it will be more muscle loss and not as much fat loss ... which could sabotage you "down the line" since it's the muscle in your body that burns more calories and keeps your metabolism (your burn rate) high. The more fat you are and less muscular, the less calories your body will burn, which makes it much harder to lose weight and maintain losses down the line.
Eating more vegies is a good way to "fill up" with bulk with not so many calories or carbs, but the carbs do add up, so measure your vegies and eat 4 cups a day of select vege's only. Any less and you may feel too hungry, any more and you may be getting too many carbs.
Skipping an IP packet, will drop your calories a little (120 to 140 or so) but also drop your protein and could cause you to burn more muscle. This will result in faster losses now (but you could find yourself plateauing later).
Not enough water is VERY BAD. Make sure you are getting 80 to 100 oz of water a day. I know this can be hard to choke down as it's a lot of water. Try putting some herb tea bags in your water (i like Cinnamon Apple Spice teabags). Some nutritionists say you should drink 1/2 oz of water per 1 pound of body weight, but this might be a tad excessive (having you drink 130 oz of water per day sounds like too much). In any case, your body needs a lot of water in order to break down and expel fat in your urine (it's actually the mechanism where your body gets rid of the fat). If you aren't drinking enough water, then your body will have a hard time burning and expelling fat. One last note on water, 50 oz of water weight 3.5 pounds -- so 100 oz of water weighs 7 pounds. So your scale weight can be significantly higher after drinking a lot of water (and before you pee it all out). This is why it's best to weigh yourself at the same time every day ... first thing in the morning (after peeing and before drinking or eating anything) is best (IMHO) as you are most dehydrated then and will give you are more consistent baseline time for your daily weigh ins. However, even doing that you weight could still fluctuate more than you think, so focus in more on your weight in 4 to 7 day blocks and don't get too hung up on daily weight numbers. All kinds of things can throw monkey wrenches in daily weigh ins (like your period, bowel fullness, water weight, or other hormonal fluctuations). I have had days when I was perfect on IP P1 and my weight went up 1 pound from one day to the next. Try not to freak out if that happens! And it will, but in a few days your weight will come back down to lower than where you started.
One more thing to try, is try to eat more earlier in the day ... and less after about 6pm. Your body burns calories more efficiently earlier in the day (since you have more of the day left to be active). After 6pm many of us get more sedentary and eating a lot of food/calories late and then going to bed soon after could sabotage you a little bit.
Now let's look at your week 2 and week 3 losses ...
WI #2 - 5 days later = 1.8 pounds, 2 inches
WI #3 - 7 days later = 1.8 pounds, 2 inches
In 5 days you lost 1.8 pounds. If we extrapolate this out to 7 days, it would have been (7/5) x (1.8 pounds) = 2.52 pounds
This is SO CLOSE to my estimate of 2.6 pounds per week for you, it's not even funny!
So your week 2 losses are right on target.
Now in week 3, it took you 7 days to lose 1.8 pounds, however if you started eating extra hard boiled eggs and extra IP packs (which is giving you more calories) ... then it makes perfect sense that it's taking you longer to lose weight. That being said you are still not that far off from my strict IP P1 estimate of 2.6 pounds per week for you. You actually lost 1.8, which is only 0.8 pounds less. Not a big deal.
It's interesting that our current weights are identical right now at 259 pounds, but I am 14" taller than you, which boosts my BMR to 1924 calories per day (almost 100 calories more a day than you). It would have been more, but I am also probably 25 years older than you, so that reduced my BMR. In any case, my past five weekly losses have been -2.0, -1.0, -2.75, -3.75, -2.50 ... which is an average of -2.4 pounds per week. This is actually pretty similar to your numbers. Even small weekly weight loss numbers can add up significantly over time!
I think the big things for you to focus on are:
1. Get more realistic with your expectations, as what you are doing now is locking you in on a "sense of failure" when you are actually having success. You are doing FINE! Keep it up.
2. Notice your INCHES LOST numbers!! Losing 4" off your measurements in 2 weeks is fantastic. This is pure fat loss (especially your waistline measurement). I have been on IP P1 a bit less than 4 months and I have melted away 11" (nearly a foot!) off my waistline, from 54" to 43". This is incredible. So try to focus on the positive.
3. Think about how long it took you to get as heavy as you are now. It might have taken years. So give yourself some time. You are only 3 weeks in. Just keep the scale pointed down, keep melting off those inches, lose the unrealistic expectations, relax and breathe, and try to be positive and happy! This diet will work ... IF YOU STICK TO IT (and don't cheat) ... not always easy. But we are all rooting for you.
4. You are down 14 pounds and 9" off your total measurements in 24 days, so give yourself a pat on the back!!! If you think about how much you've lost in the past 3+ weeks, it's pretty miraculous.
5. One last thought, deviating from the plan is a slippery slope (IMHO). At least for the first 3 months, try to follow IP Phase 1 100%. Don't eat less than what is laid out, and don't eat more. Don't try to "wing it" on your own. Just follow it, it will work. It's your time, it's your money, and it's your body. But why not try to maximize your losses while you are focused on losing!