Could you post a photo of the whole tank?
Seems like you have high nitrates and low or no CO2. Feed less, do frequent WC, add CO2 and add fast growing plants (i.e. guppy weed, water sprite, pothos, salvinia, etc). Also, you should have at least a flow rate of 3-4 times the size of your tank. That means you should upgrade your filter. A hang on back or a canister filter with a flow of 400-500 l/h would work. You can always reduce the flow of a filter, but you can't increase it.
One way to eradicate BBA is, like Paraguay said, to remove as much as you can. Turn off your filter and any circulation in general. Use a stiff toothbrush or manually remove BBA from wood and rocks, and syphon any dislodged algae immediately. For plants, use the toothbrush, or if it's only a few leaves, cut them. Do a WC. Add filter floss to the filter. Turn your filter back on. Replace the filter floss the next day. Do that as many times as needed. It could take weeks to totally remove it though. Or never, if you don't deal with the actual problem.
The other way is too drastic and you could lose your livestock. You can kill BBA by spot treating it (use a turkey baster or a syringe) with excel or hydrogen peroxide 3%.
For the excel use the manufacturer's recommended dose. Turn off your filter and slowly squirt the excel onto the algae. Let it sit there for about 10-15 mins and then turn your filter back on.
For H2O2, use 1mL per 5 litres of water. Same procedure as above. Some do it that way, dose it directly to their tank or remove enough water so that the spot with BBA is out of the water.
But the safest way is to take the infected plants or hardscape out of the water and spray them. For plants, let them soak for 3 mins and wash them with tap water.
I've never spot treated or dosed H2O2 directly in my tank. However, I used to have a saltwater aquarium and I did spray it on live rock to kill some bryopsis (after I removed the rock from the tank of course) and it did work.
Good luck!