How do you picky eaters eat good and lose weight?

I'm a really picky eater too. There are a few things you can do...

Eat the things you like but in small portions.
Substitute your lunch on the weekends for example for something unhealthy which you like, but keep the other two meals healthy.
Cut out as much fat as you possibly can.
Eat more protein and less carbs or cut the carbs out completely and add a bit more fat instead for taste.
Introduce new and healthy foods a little at a time and have them together with things you already like. For instance if you like meat with bearnaise sace, have some broccoli, mushrooms, carrots, cabbage, onions, bell peppers, or whatever vegetable you want but cut out the fries or pasta from that meal.
Taste the things you don't think you'll like together with a sauce or soup or stew or put salt or calorie free flavor enhances like mustard and hot sauce on them to tone down the new taste.
Eat more protein and vegetables to make your stomach full and you won't be as likely to want to go looking for unhealthy snacks after dinner, even if you weren't crazy about what you ate and therefore didn't feel completely satisfied.
Most importantly just try not to judge foods until you taste them. Keep and open mind and never say no to trying something new, even if you don't think you'll like it.

My mom never forced me to eat or taste anything I didn't want, so I've had to discover a lot of it as an adult. It makes it a bit harder, but not impossible. I have a weird fobia of everything which has fat-like texture and I cannot stomach the taste of strong tasting fish like salmon. Still, I'm trying to experiment and grow, and I can now eat mushrooms, shrimp and such, even though they're not my favorite thing, and I've even eaten eel and squid (and the squid was fresh and really not fishy or rubbery at all)!
You can let yourself feel reluctant and still push through. It's okay to take your time with new food, as long as you give it a try.

I'm a picky eater. I'm also super-sensitive to certain flavors, textures, or smells, i.e. there are certain foods that, if I put them in my mouth, I will instantly puke up everything I've eaten in the last ten years, including but not limited to: cooked carrots (raw are fine), mushrooms (texture issue), and raw red tomatoes (I substitute tomatillos if I can).

That being said, I'm also fairly adventurous, and willing to try new things. Some get added to the pukey-list (asparagus). Some I just don't like (I hate sushi. I hate yogurt. I can tolerate avocado if it's a minor ingredient). Some are new favorites (quinoa).

Here are my suggestions, hopefully one of them will work for you:

Most veggies are exponentially tastier raw, rather than cooked.

Since texture is a huge issue for me, cooking things in a different way can change everything. I can't eat mushrooms normally (though I *do* enjoy the flavor), but if they are cut small enough, and mixed with enough other foods, I can eat them just fine.

I cannot eat cooked carrots yet, though I keep trying different things: cooked with different ingredients, steamed instead of boiled, et cetera. I've only ever managed to eat small amounts when diced up extra-small and mixed with lentils and rice and plenty of spices.

I've adapted a tiny bit to red tomatoes, simply because in the US we are compelled to put ketchup and ketchup-adjacent "sauce" on *everything*, but I will, for example, order pizza with *minimal* sauce or no sauce (or white sauce, if I'm at a higher-end pizza place), specify 'no tomatoes' when I order, or pick out raw ones if there is no other choice. Or order something with enough other ingredients that the tomatoes blend in instead of remove all food from my stomach in a colorful manner.

If I'm cooking, I will add onions (green or white or red or whatever, I love all of them) or green bell peppers or whatever chiles are on hand or garlic or something to make it more palatable. Celery and cucumber get used a lot in my kitchen, too. Cilantro. Green sauce (yes, made from tomatillos) can make a lot of foods edible for me that aren't otherwise. Same with garlic sauce and, of course, cheese (though I try not to do that last too often). If you don't like any of these, find something you do like, and try mixing with that instead.

Learning to use spices helps a lot. And if you don't like 'hot' spicy food, look up how to use cinnamon or nutmeg or similar for a 'sweet' spicy instead.

It may just take time to find something that works for you.

Good luck!