As a vegetarian..
No, vegetarians/vegans do not lose a lot of weight. You can eat very healthily though and maintain a healthy weight. Though it's often hard to always eat enough to stay full and it's easy to overdo it on the carbs. I know veggies and vegans of all shapes and sizes, they're not all skinny! I found it hard to make sure I ate enough when playing 80+ mins of rugby, but that might just be me.
If you choose to be vegan, then it usually the lack of dairy and eggs that causes the problems. However, you do not have to be ill or lacking anything, just need to make sure you get enough protein and calcium etc. which are essential to your health.
Yeast extract spreads, like Marmite or Vegemite, or yeast flakes are often used in vegan cooking, so I think they're fine, but it's all personal choice. Vegans may not eat bread as sometimes it contains milk extracts.
True veggies/vegans will not eat anything containg gelatine, cochineal, animal rennet (in cheese), wine/beer purified with isinglass, Worcestershire sauce (contains anchovies, although vegan versions now available) etc. etc.
Being veggie/vegan you can be as healthy or unhealthy as you choose. If you live off chips, it mya be a vegan diet, but probably not the best. However, it does encourage you to try a range of vegetables, pulses, beans, grains, tofu, seitan, tvp etc. etc.
If you want to lose weight you need to consume more than you consume, i.e. use up more calories than you put in your mouth. Though you shouldn't get too hung up on weight, i.e. the mass of your body. It's about how you look and feel and how well your jeans fit, not what the scale says.
Also, if you go veggie or vegan you need to think about your diet to ensure it is well-rounded, but nowadays it is not that hard.