Uneven VTF on different part of same LP

From the information supplied, some possible causes include:
1. with most tonearms, including yours, a non-level tonearm bearing vs. a level LP surface would result in a gradual change in VTF as the tonearm arcs across the record;
2. differing position of the tonearm wires as the tonearm arcs across the record could cause VTF changes;
3. dirty tonearm bearings; and/or
4. worn tonearm bearings.

Only #4 would require replacing or seriously rebuilding the tonearm. If you're happy with it otherwise, a thorough diagnostic to identify the actual cause(s) of the changing VTF would be in order prior to expending significant monies.

Start by checking the arm's freedom of movement. Reduce VTF to zero and disengage anti-skate so that the arm/cart floats free and level. Brush the arm gently inward and outward with a feather or a breath of air. It should move freely and equally in both directions. Any resistance could be evidence of 2, 3 or 4 (or a combination thereof).

P.S. A unipivot is still subject to 3, 4 and (especially) 2. There's no reason to believe a unipivot would automatically eliminate your problem.

(1) How accurate is your scale?
(2) How accurate is your level?
(3) We have too much faith in manufacturers and subsequently believe that their products are manufactured perfectly. Not so. Unless you're willing to spend big bucks on products manufactured to "precise standards, these types of issues will always crop up.
(4) If your bearings are worn/not perfectly round, that is another issue.
(5) How accurate is your set-up, considering all of the above.

Vinyl reproduction requires a lot of thought, proper set-up and products manufactured precisely in order for the end user to obtain satisfactory performance.

Further I put bubble level on the tonearm's bearing housing, it showed unlevel (the turntable itself is perfecty even) which might cause the above issue.

Well, when an Armboard is not level, you will ruin your cartridge pretty fast.There are so many different forces for it, it can't survive. Your cantilever will be bent sooner or later. Well, of course it is possible that you have also different VTF based on that, but the other problems are much more serious. Did you also hear a shifting in soundstage in the last 3 tracks?
Is it a DIY board?

If you have a digital scale it might be a good idea to change the batteries. Best of Luck and post up and let us know if you find the problem.

Not much to add, except:
1. Check the accuracy and precision of the balance. If it's accurate to within +/- 0.02 gms, a difference of 0.04 could be within spec (0.02 gms on either side of the actual value) and actually indicate the same "real" value.
2. Along the same lines, do you know how the balance's read-out handles intermediate values? A displayed value of 1.704 might be 1.7044, 1.705 or 1.706, depending on how it rounds. It might even be as much as 1.709 if it just truncates the last digit. Combining rounding and precision issues could make finding whether there is a "real" or only an "apparent" issue difficult to sort out.
3. How many measurements did you make? It would not be unusual to have some variation when you are looking at such small VTF differences. Any good scientist using an analytical balance would take several readings. Given the potential for either explanation 1 or 2 to be an issue, I would take 5 or 10 separate readings at each location, average them, and then compare the two averages. If the variation between the highest and lowest of a set of readings is greater than the specs for the device, then it might just indicate a problem w the device. In that case, I'd borrow another balance and re-check.
4. Are you able to take the measurement with the balance in the same horizontal plane at both places along the tracing arc? If not, that could also introduce some error into the readings.

Given the relatively poor quality control we have all seen in manufacturing over the last 20 years or so, I would not jump to any conclusions. I'm not trying to make you crazy, but you should be aware that there are a number of reasons why the difference you reported may not be "real". Before you tear your hair out looking for a problem that might exist, or you pay major $ for a rebuild or a new arm, you'd be well advised to sort through the "error tree" on this. Personally, I would be more concerned with the out of level issue, but of course some of the same questions would apply to that measuring device. For example, how "flat" is the case of the level itself. Or for that matter, how "flat" are the surfaces of the bearing housing and platter that you are placing the bubble on?

Maybe the easiest solution is to ask Dougdeacon to come over for a listen; he can hear differences of 0.01 gms (no data that I aware of regarding how many degrees off nominal his ears can discern). Or you could look to address all of the reasonably likely causes of your observations. If you find none, and you continue not to hear a problem, maybe there is none. In that case, just relax and enjoy the tunes! Good luck.