Please recommend compact chess set for analysis

This one maybe:

It's a new Chavez set, it's weighted and felted.

http://www.variantes.com/pieces-jeu-echecs-classiques/1761-pieces-d-echecs-chavet-plombees-feutrees-n3-01213.html

This could be a good option. A Dubrovnik plastic Analysis set.

http://chessgamesshop.com/index.php?c=13&p=586

Ships from Slovenia. Not sure about weighting, maybe you could write to them about it.

Is being able to put the set away safely with a position still set up on the board a consideration?

If so, and if you're willing to consider pegged sets, you could do worse than consider antiques- eg:

https://www.ebay.co.uk/itm/Whittington-Travel-Portable-chess-Set-slide-lid-model/233139848710?hash=item364837c606:g:0rwAAOSw8b9bgtGJ:rk:2:pf:0

or this sort of thing (I have a couple of these and they're really nice):

https://www.ebay.co.uk/itm/John-Jaques-Whittington-Travel-chess-Set-1890-Read-Description-/264168365836?hash=item3d81a95f0c%3Ag%3AqJcAAOSw5atbu4nj&nma=true&si=3B8zEUxwlXTSjUlUKtorpYCO3gg%253D&orig_cvip=true&nordt=true&rt=nc&_trksid=p2047675.l2557

ChessBazaar offers free shipping.  Maybe one of these would fit the bill:

https://www.chessbazaar.com/travelling-chess-set.html?price=100-

I just ordered this one along with a 45mm square size board.

For something unusual at a reasonable price you might like this one.  They also have a black and natural set that is in stock.

https://www.chessbazaar.com/reproduced-vintage-1930-german-knubbel-chess-set-in-stained-crimson-and-boxwood-3-king.html

That German Knubble set is cute beyond words!

Gg

The Chessbazaar site says the set with the red pieces would be able to ship the end of February.  The set with the black pieces are available now.  I ordered a different set from Chessbazaar a couple of weeks ago and it took only 4 days to arrive at my house. 

In the UK....

https://www.regencychess.co.uk/folding-amp-travel-chess-c-4.html

Always liked the Knubbel set, too! Nice to see that Chess Bazaar is doing an ebonized version of it also. It's easy to see why Bent Larsen liked it as any analysis set. Very sturdy!

You literally can buy vinyl boards and plastic pieces all over Europe. Why order from the US?

a5zima, the Chessbazaar Knubbel set comes in a glossy lacquer finish for an extra $29.99.  Buff polish is the standard finish.

This may be something to consider as an inexpensive alternative:

https://www.amazon.com/dp/B07MGC18WF/ref=twister_B07MXHXT63?_encoding=UTF8&th=1

House of Chess offers a few library size sets for an affordable price.

3" and 3 1/4" sets are very affordable in my opinion.

http://www.houseofchess.com/wood-chess-pieces.html#seo_title=Wood+Chess+Pieces&top_cat_id=2&sel_cat_id=8&sort_by=price-0&chk_sub_cat_id%5B%5D=8&page_num=1

They have several versions of this, with and without weights. The sets are identical hollow plastic, in the weighted ones the weights rattle - apparently they are supposed to be held in place with wax, but the wax breaks up. 

I own both types, one set with weights one without - I kind of like them, but, they are extremely cheap sets and it shows in every way.

This is probably not the answer you are looking for, but I think it may help you in some way.

In order to help you better, it may be a good idea for you to articulate why you need your analysis set to be smaller than a standard tournament set.

Do you lack the table/desk space needed for a full size set?

Or, do you plan to use your analysis set as your travel or on the go set? 

I too once wanted an analysis set that was smaller than the standard set. I thought it would save me counter top space, and still be useful if I wanted to go to a coffee shop or travel anywhere with it. 

I ended up buying a very niece analysis set that is exactly like a tournament plastic set, but a third the size. The board is a vinyl one that is also about a third the standard size. In theory it was a good idea. But in practice, I ran into a few problems. 

First, smaller pieces mean smaller base diameters, which in turn make the pieces easier to knock over while playing. This is exacerbated by the facts that 1) smaller squares mean the pieces are crammed closer together. 2) The pieces are much lighter and 3) They are not magnetized. 

Trying to play with it in a park with even a bit of wind, was not fun. 

Aside of how easy it is to knock the pieces over, I also found that I personally enjoy the “sensory” experience of chess a lot more than I thought. The feel, weight and look of full size pieces makes it more enjoyable for me to sit there and study for longer periods. 

I now use one of my nice, tournament size wooden sets with a vinyl or mouse pad board at home for studying with books. It still only takes one sitting space at our dining table or at my desk. Not much of a difference there. I also have a magnetic wooden folding set for when I travel anywhere for vacation, as well as a small magnetic flat pocket set for when the chess bug bytes me at the Dr’s office, or during my lunch break from work. Bottom line is, I don’t use my “analysis” set at all anymore. 

I’m not trying to discourage you from buying something you may end up liking and using. 

I just thought my experience in this area may be of use in your decision making process. 

Good luck. 

Left to right:

Standard tournament size - 2.25 inch squares, 3.75 inch king

1 7/8" (1.875") squares board with notation borders cut off, 3.5 inch king

1.5 inch squares board with borders cut off, 2.7 inch king

For portable choice I very much prefer the 1.875" board with 3.5 inch king, smaller than that and I think you really need to choose a magnetic set or you will constantly knock pieces over. It is less width than my shoulders so if there is no space for it, there is no space for me to sit either.

If you prefer your board less crowded you can get 3.5 inch sets with smaller bases, in fact such sets are more common, however, piece stability becomes an issue as you go to a smaller board and I prefer the wider bases of this set.

Here is my 3 1/4 inch Sovereign Staunton in Golden Rosewood from houseofchess.com

The board is a folding magnetic tournament #5 board with 2 inch squares from ymimports.com