Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Americans pronounce weightlifting as WAYT-lihf-tuhng (/ˈweɪtˌlɪftəŋ/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The barbell is used for heavy weightlifting exercises".
Record yourself saying "weightlifting" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 9 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Start with your jaw slightly open and the front of your tongue forward and slightly up. Glide upward, your jaw closes a little more and your tongue arches higher toward the roof of the mouth.
Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

Place the tip of your tongue against the alveolar ridge just behind your top front teeth, the same contact point as /t/, /d/, and /n/. The difference is what happens to the air: for /l/, you let it flow continuously around the <em>sides</em> of the tongue (that's why /l/ is called a lateral). Turn your voice on the whole time. Lips stay relaxed, no rounding or flaring. For the Dark L variant at the end of a syllable, also pull the back of the tongue up and back toward the soft palate.

Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

Lift your bottom lip to touch the very bottom of your top front teeth. Blow air through this contact point without voicing.

Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Lift the back of your tongue to the soft palate. Lower your soft palate to let air flow through your nose.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "weightlifting", the "t" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the first syllable, not the others. Stretch WAYT — keep everything else short and quick.
Don't pronounce the second syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.