Your Ultimate Gardening Guide.
Rules
This is my second year trying to grow tomatoes on my balcony. Last year went alright but had some end rot on my romas. This year all 3 of my tomatoes have leaves that are turning brown like this. Can anyone tell what would cause it?
What fertilizer have you used?
What kind of soil do you have them in, and how often are you watering them?
We've had rain and cold weather the last week or so. The soil has been wet when I've touched it so I haven't manually watered them recently.
The soil is all purpose miracle grow
You don't want to use that junk on tomatoes, especially in containers. You want a soil that is meant for outdoor containers OR raised beds. It should have a sandy consistency, and dry out easily between waterings every 2-3 days.
You also want a slow release fertilizer for tomatoes and vegetables plants. It's essentially processed and dried manure and other plants material that breaks up and feeds your tomatoes over 4-6 weeks at a time. During the summer you'll apply 2-3 times, and that will keep them pretty balanced on the nutrient front.
Looks to me the issue is the soil here here.
Bag soil tends to retain too much water. Has the soil been saturated for days?
Yes
Yeah that'll do it. I'd dig them up, remove any rotted roots, fix the soil, and repot. Plenty of options like perlite, coarse sand, tree bark. And make sure you don't compact the soil by packing it down when potting.
Edit: also the other question about fertilizer. Could be too much. Likely not too much sun, since you said it's been cold and rainy.
Do your pots drain?
The other two 
@Custard to me it looks like sunburn. If u don't harden off your young plants by introducing them to the sun a few hours a day, then longer, etc before planting, they can get sunburn/sunscald. My fig tree got it this year when I brought it out of the garage for too many hours at once. Peppers can get it too. Keep watering regularly, maybe use some Epsom salt watering once in awhile too. New leaves will grow, the damaged will die. My 2 cents.
Soil looks pretty wet and the pot quite small.