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I have found \uwave in the ulem package, and its definition in ulem.sty:

% Now define various special underlines.  All the definitions go like
% \def \command {\bgroup \markoverwith{something} \ULon}

% For drawing a wavey underline instead of a straight one the command
% is \uwave (under-wave) which uses the wiggle from 6-pt lasy font:

\def\uwave{\bgroup \markoverwith{\lower3.5\p@\hbox{\sixly \char58}}\ULon}
\font\sixly=lasy6 % does not re-load if already loaded, so no memory problem.

I would like to keep the underline wave, but much thicker, does anyone know how to do it?

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There is a bold variant of the lasy fonts: lasyb10. Some scaling is needed to fit the width of the character of font lasy6 (e.g., because of different design size).

The example is plain TeX syntax, therefore I keep it.

% plain TeX    
\input ulem.sty\relax
\catcode`\@=11 %

\font\uwavefont=lasyb10 scaled 652


\uwaveold{Hello World}

\uwave{Hello World}


Compare the result:

uwave with lasy6 and lasyb10

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