You named two separate problems;
1. Weak; if that means low volume / lower output than the other strings, the possible causes / solutions; Strings, pickups, pickup height, onboard preamp / EQ, amp, speaker cab.
2. Floppy; if that means the B string seems to have a lot less tension than the other strings, the possible causes / solutions; string, setup.
If your bass rig starts rolling off at around 48Hz and is down 3-4db at 35Hz, most bass B strings will sound weak on notes below the 5th fret through that rig.
If your bass is set up with the action @ 3/32” at the 12th fret all the way across with about 0.005” neck relief at the 8th fret, the B string (and likely a few other strings) will feel like Pahoehoe poly strings on a 20” scale ukulele bass.
A poor B string doesn’t know what bass it’s on if it’s between two witness points 34” apart & tensioned up to the vibrating pitch of about 31Hz. It also doesn’t know what pickups are under it and how far away the frets are.
When these threads come up, you see those that have a 34” scale bass with a no-good B string, and a few dozen that have a 34” scale bass with a great B string. Both circumstances can exist with different strings, pickups, setups, amps & cabs. Your B string output could be weak because the string is so floppy its vibration is choked out from hitting the frets. That’s still a setup &/or string cause / solution.
Jack up the action on the B where you know it’s not fretting out, raise the pickups up closer to the B, play it kinda hard. If it’s still weak, try it on another bass rig if possible. If the E & A strings sound good, and the B is from the same set, you can probably start thinking, pickups, setup, amp, cab.
The solution exists. Good luck.
