The largest prospective study that I am aware of in the EPIC-PANACEA study which has followed over 373,000 men and women over 5 years  and recruited subjects between the years 1992 and 2000 in 10 European countries
Our objective was to assess the association between consumption of
total meat, red meat, poultry, and processed meat and weight gain
after 5 y of follow-up, on average, in the large European population
who participated in the European Prospective Investigation into Cancer
and Nutrition-Physical Activity, Nutrition, Alcohol, Cessation of
Smoking, Eating Out of Home and Obesity (EPIC-PANACEA) project.
This showed that even adjusting for calories, you were more likely to gain weight when eating meat or poultry.
Total meat consumption was positively associated with weight gain in
men and women, in normal-weight and overweight subjects, and in
smokers and nonsmokers. With adjustment for estimated energy intake,
an increase in meat intake of 250 g/d (eg, one steak at approximately
450 kcal) would lead to a 2-kg higher weight gain after 5 y (95% CI:
1.5, 2.7 kg). Positive associations were observed for red meat, poultry, and processed meat.
They then looked to see if fruit and vegetable intakes influenced weight change but there was only a weak association between failure to gain weight in women who gave up smoking.
In this large study, higher baseline fruit and vegetable intakes,
while maintaining total energy intakes constant, did not substantially
influence midterm weight change overall but could help to reduce risk
of weight gain in persons who stop smoking. The interactions observed
in women deserve additional attention.
As to why those who consume meat tend to gain weight, whereas those who don't are less likely, it has been shown that the intestinal microbiota differs in omnivores 
Vegetarians had a 12% higher abundance of bacterial DNA than
omnivores, a tendency for less Clostridium cluster IV (31.86 +/-
17.00%; 36.64 +/- 14.22%) and higher abundance of Bacteroides (23.93 +/- 10.35%; 21.26 +/- 8.05%), which were not significant due to high interindividual variations. PCA suggested a grouping of bacteria and
members of Clostridium cluster IV. Two bands appeared significantly
more frequently in omnivores than in vegetarians (p < 0.005 and p <
0.022). One was identified as Faecalibacterium sp. and the other was 97.9% similar to the uncultured gut bacteriumDQ793301.
One current thought is that the bacteria in the gut of a human omnivore is more able to metabolise food releasing nutrients otherwise unavailable to vegetarians. This might account for about 2% of the daily food intake, and works out to be about 5 lbs of weight gain a year.
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