[T3] Hard Starting

[J. Jonik]

Re/ 71 T-2 Std.   It's been cold out so maybe some starting problems happen...but, my battery checks out Good at the Auto Shop.- Once when start attempt got weaker and weaker, a neighbor loaned me his Jump Start thing and car started right up.- Went home and put battery on overnight charge...even though my gravity tester thing showed all cells right up to the top.  Started good in the morning...with warm battery anyway.- Later that day starting got a little sticky again...cranked, cranked, then started. That's when I went to get battery checked at an auto store.  Battery good.- Next day...hard to start again...but it did.
So....question is, can there be something funny in the car itself that's maybe weakening the battery after sitting overnight or even for maybe five hours in daytime?    Any way to test for some little juice drainage when car (and radio and everything) is off?
Does success of the Jumper Box tell us that the starter's ok?
Didn't yet put in new clean fuel filter.   Does that have bearing on the case?
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