A moderate amount of water while eating will not dilute digestion
...according to Michael F. Picco, M.D. and the Mayo Clinic:
There's no concern that water will dilute the digestive juices or interfere with digestion. In fact, drinking water during or after a
meal actually aids digestion.
Water and other liquids help break down food so that your body can
absorb the nutrients. Water also softens stool, which helps prevent
Water, after all, is the "universal solvent" which should help break food and organic materials down further.
Effect of Stomach Acid Dilution
This is a total myth, especially if you consider it from totally a chemical perspective. Stomachs secrete about 400 to 700 mL of gastric acids per meal. Just to be conservative, let's say 500 mL. Also, the average stomach has a pH of about 2. Now let's look at the formula for pH and what the effects of adding water might be:
pH = log(1/(mols/volume))
2 = log(1/(mols/0.5L))
Now solve for mols, and we get
mols = 0.005
Now let's assume our meal contains about a quarter of a liter of water in it. We'll also assume that our food is completely pH neutral. This is probably a little high on water concentration, but let's see its effect on our stomach's pH.
Since it has a neutral pH, the mols does not change, but our volume does (0.5L [previous contents] + 0.25L [from the food] = 0.75L).
pH = log(1/(0.005 mols/(0.5L + 0.25L)))
Now solve for pH and we get
pH = 2.18. No problem here, since normal digestion occurs between a pH of 1.5 to 3.5.
Finally, let's say we drink a lot of neutral pH water with our meal now.
pH = log(1/(0.005 mols/(0.75L + 4.25L)))
pH = 3
So we are still within a normal pH of digestion, even though we just drank over 4.25 liters (~1.12 gallons) of water with our fairly liquid meal of 0.25L! We would need to drink about another 45 L of water to knock our gastic pH above 4. But don't worry, we would die of water intoxication well before that ever happens.
Furthermore, our stomachs (and digestive tract) are incredibly good at adapting their secretions to the consistency of a meal.
Water and Speed of Digestion
Perhaps another way that water may change caloric intake is to increase the speed at which solid foods exit the stomach.
This is thought to reduce the meal’s contact time with stomach acid and digestive enzymes, resulting in poorer digestion.
As logical as this statement may sound, no scientific research supports it.
A study that analyzed the stomach’s emptying speed observed that, although liquids do pass through the digestive system more quickly than solids, they have no effect on the overall solids’ digestion speed.
Water during meals should not decrease the amount of calories absorbed. With all that being said, digestion is a very complex system, and there are still many unknowns as well as individual responses. Before making drastic changes concerning your health and digestion, you should consult a medical professional. This answer should in no means necessary replace any medical advice or treatments, but rather aid in your understanding of how digestion works.
A Final Word of Caution
I feel obligated to include that however you found this question/answer, staying hydrated to aid in digestion is a very healthy function, especially in considering weight loss and 'feeling full for longer.' However, obsessive water consumption aimed at decreasing food consumption/appetite ("fluid loading" or "water loading") is a common symptom of eating disorders. If this is a concern for you or someone you know, please, seek professional support and help.
NCBI - Adaptive Secretions
NCBI - Digestion Speeds