Well batteries aren't usually rated by weight!
They spec AH and CCA.
AH is amps per hour that it can supply. My scoot uses a 10 AH battery
(probably a 5 pounder). This tells you how fast you can charge it and
how much extra capacity you have for running things beyond the power
your bike makes.
I could buy a 12 AH (if it will fit) and that would be a 7 pounder. It would
allow 2 amps more power or 24 watts (amps x volts). This extra capacity
is used say on a dark and cold night when you have your lights and heated
grips on and are going slow so not making much juice.
The CAA is cold cranking amps. A battery looses ability to supply power
when cold. It might supply 300 amps at 70F and only 190 amps at 32F.
The CCA is how much it can supply at 32F.
There are several ways to build a battery. The old fashioned lead acid just
floats lead in an acid bath. The AGM fills the liquid with Glass Mat material.
This makes the battery more consistent so it can supply more current and
last longer when drained.
So your 5lb might be AGM and have 8AH but 200 CCA (more CCA so can try to start longer)
and your 7lb might be lead acid and have 10AH but 150 CCA (more AH so can run more/longer
on dark night with extra lights on)
Thus you can't go by weight but instead you need to check AH and CCA
(and type).
There are other types beyond lead acid and AGM, like lithium and gel each
has unique qualities (and prices).